DO NOT DELETE THIS SECTION
Calculus II
MAT251 | 4 Credits
Calculus II will help you expand your understanding of the principles of calculus, including techniques of integration and logistic models. You'll also study parametric and polar coordinate systems, explore infinite sequences and series, and apply integration techniques to solve problems like calculating work and analyzing curve behavior.
Professor: Ms. Sayali Desphande
About This Course
What You’ll Learn
Expand on what you learned in General Calculus I with our online General Calculus II course, which covers the techniques of integration, application of integration, exponential and logistic models, parametric equations and polar coordinates, sequence and series, and vector and geometry.
- Solve integration problems using different techniques of integration: integration table, u-substitution, trigonometric functions, partial fractions, trigonometric substitution, and trapezoidal rule.
- Apply integral calculus to compute average value of function, volumes, arc lengths, surface of revolution, and work, as well as moments and centers of mass.
- Use various tests to determine the convergence and divergence of sequences and series.
- Apply Taylor and Maclaurin series for polynomial approximations.
- Demonstrate convergence and divergence of power series.
- Solve homogeneous differential equations.
- Use differential equations to solve ‘Growth and Decay’ problems.
- Sketch parametric and polar curves.
- Apply differentiation and integration to parametric equations and polar functions.
- Apply dot product and cross product to vectors in R2 and R3.
- Apply differentiation to vector functions.
StraighterLine Courses Include:
-
Self-paced workload
-
Digital Textbooks
-
Transcript Delivery
-
Grade Improvement Opportunities
-
Interactive Modules
-
Video Lessons
-
24/7 Tutoring & Support
-
Access on Desktop and Mobile
Transfer Credit in 3 Easy Steps
Pick Your Course & Enroll
Getting started is simple — no applications, waitlists, or deadlines. Just create an account, choose your course, and start learning right away.
Every course is self-paced and fully online, so you can fit learning into your life — not the other way around. With support resources included and no hidden fees, you're in control from day one.
Go at Your Own Pace
No rigid schedules, no stress. Just real online college courses you can start anytime, anywhere, and finish on your own terms.
StraighterLine courses offer interactive lessons and assignments that help you understand and retain the material, and come with everything you need to stay on track and succeed — including digital textbooks, tutoring, and real people to support you on your journey to your degree.
Transfer Your Credits, Save Thousands on Tuition
Complete your course with a 70% or higher to make your credits eligible for transfer. Then head to your Student Dashboard, select “Request Transcript,” and tell us where to send it — we’ll take it from there at no additional cost.
Not sure whether your school accepts StraighterLine courses? Our Enrollment Specialists can find out for you!
Does My School Accept This Course?
We’ll find out for you. Students have successfully transferred StraighterLine course credits to 3,000+ schools. Our Enrollment Specialists will contact your college directly to confirm your credits will transfer, so you don’t have to.
WANT US TO CHECK?Course Details
This course is designed to build on students' knowledge of the principles of Calculus. This includes techniques of integration, application of integration, exponential and logistic models, parametric equations, and polar coordinates; sequence and series; and vector and geometry.
ACE-Recommended
ACE Code:
OOSL-0019
Flexible Schedule
30-day Average Course Completion
Mathematics Courses Have Transferred Over 10,600 times
$600,000 Saved on Tuition
Prerequisites
Calculus I is a required prerequisite for this course. If you enroll, the assumption is made that you have previously completed Calculus I for credit with a passing score.
Course Text
This course does not require a textbook.
Course Checkpoints
An Introduction to Calculus II
- Welcome to Calculus II
- Review: Calculus I in 20 minutes
Techniques of Integration
- An Introduction to the Integral Table
- Making u-Substitutions
- An Introduction to Integrals with Powers of Sine and Cosine
- Integrals with Powers of Sine and Cosine
- Integrals with Even and Odd Powers of Sine and Cosine
- Integrals of Other Trigonometric Functions
- Integrals of Odd Powers of Tangent and Any Power of Secant
- Integrals with Even Powers of Secant and Any Power of Tangent
- Repeated Linear Factors: Part One
- Repeated Linear Factors: Part Two
- Distinct and Repeated Quadratic Factors
- Partial Fractions of Transcendental Functions
- Trigonometric Substitution
- Converting Radicals into Trigonometric Expressions
- Using Trigonometric Substitution to Integrate Radicals
- Trigonometric Substitutions on Rational Powers
- An Overview of Trigonometric Substitution Strategy
- Trigonometric Substitution Involving a Definite Integral: Part One
- Trigonometric Substitution Involving a Definite Integral: Part Two
- Numerical Integration
- Deriving the Trapezoidal Rule
- An Example of the Trapezoidal Rule
Applications of Integral Calculus
- Finding the Average Value of a Function
- Finding the Volumes Using Cross-Sectional Slices
- An Example of Finding Cross-Sectional Volumes
- Solids of Revolution
- The Disk Method along the y-Axis
- A Transcendental Example of the Disk Method
- The Washer Method across the x-Axis
- The Washer Method across the y-Axis
- Introducing the Shell Method
- Why Shells Can Be Better Than Washers
- The Shell Method: Integrating with Respect to y
- An Introduction to Arc Length
- Finding Arc Lengths of Curves Given by Functions
- Finding the Area of a Surface of Revolution
- An Introduction to Work
- Calculating Work
- Hooke’s Law
- Center of Mass
- The Center of Mass of a Thin Plate
Sequences and Series
- The Limit of a Sequence
- Determining the Limit of a Sequence
- Monotonic and Bounded Sequences
- An Introduction to Infinite Series
- The Summation of Infinite Series
- Geometric Series
- Telescoping Series
- Properties of Convergent Series
- The nth-Term Test for Divergence
- An Introduction to the Integral Test
- Examples of the Integral Test
- Using the Integral Test
- Defining p-Series
- An Introduction to the Direct Comparison Test
- Using the Direct Comparison Test
- An Introduction to the Limit Comparison Test
- Using the Limit Comparison Test
Sequences and Series (continued)
- Inverting the Series in the Limit Comparison Test
- Alternating Series
- The Alternating Series Test
- Estimating the Sum of an Alternating Series
- Absolute and Conditional Convergence
- The Ratio Test
- Examples of the Ratio Test
- The Root Test
- Polynomial Approximations of Elementary Functions
- Higher-Degree Approximations
- Taylor Polynomials
- Maclaurin Polynomials
- The Remainder of a Taylor Polynomial
- Approximating the Value of a Function Taylor Series
- Examples of the Taylor and Maclaurin Series
- New Taylor Series
- The Convergence of Taylor Series
- The Definition of Power Series
- The Interval and Radius of Convergence
- Finding the Interval and Radius of Convergence: Part One
- Finding the Interval and Radius of Convergence: Part Two
- Finding the Interval and Radius of Convergence: Part Three
- Differentiation and Integration of Power Series
- Finding Power Series Representations by Differentiation
- Finding Power Series Representations by Integration
- Integrating Functions Using Power Series
Improper Integrals
- The First Type of Improper Integral
- The Second Type of Improper Integral
- Infinite Limits of Integration, Convergence, and Divergence
Differential Equations
- Solving Separable Differential Equations
- Finding a Particular Solution
- Direction Fields
- Euler's Method for Solving Differential Equations
- First-Order Linear Differential Equations
- Separating Homogeneous Differential Equations
- Change of Variables
- Exponential Growth
- Logistic Growth
- Radioactive Decay
Parametric Equations and Polar Coordinates
- An Introduction to Parametric Equations
- The Cycloid
- Eliminating Parameters
- Derivatives of Parametric Equations
- Graphing the Elliptic Curve
- The Arc Length of a Parameterized Curve
- Finding Arc Lengths of Curves Given by Parametric Equations
- The Polar Coordinate System
- Converting between Polar and Cartesian Forms
- Spirals and Circles
- Graphing Some Special Polar Functions
- Calculus and the Rose Curve
- Finding the Slopes of Tangent Lines in Polar Form
- Heading toward the Area of a Polar Region
- Finding the Area of a Polar Region: Part One
- Finding the Area of a Polar Region: Part Two
- The Area of a Region Bounded by Two Polar Curves: Part One
- The Area of a Region Bounded by Two Polar Curves: Part Two
Vectors and the Geometry of ℝ² and ℝ³
- Coordinate Geometry in Three-Dimensional Space
- Introduction to Vectors
- Vectors in ℝ² and ℝ³
- An Introduction to the Dot Product
- Orthogonal Projections
- An Introduction to the Cross Product
- Geometry of the Cross Product
- Equations of Lines and Planes in ℝ³
- Introduction to Vector Functions
- Derivatives of Vector Functions
- Vector Functions: Smooth Curves
- Vector Functions: Velocity and Acceleration
Assignments & Grading
Your score provides a percentage score and letter grade for each course. A passing percentage is 70% or higher.
Assignments for this course include:
- 3 Graded Topic Reviews
- 3 Graded Quizzes
- 3 Graded Exams
- 1 Graded Final
This course has an open book proctored Final Exam. Scientific and/or graphing calculators are allowed throughout the course.
What You’ll Need
- A reliable computer or laptop
- Stable internet connection
- Web browser
- Basic computer skills
- Scientific or graphing calculator
- Any required course materials
Your Academic Team
Your Faculty Team
We’re not just a platform — we’re a team of professional educators committed to your success. Our courses are built by academic professionals who are leaders in higher education, and your assignments are graded by real people who provide meaningful feedback so you can keep progressing.
Support Team
At StraighterLine, there are real people working behind the scenes to guide you through every course, quiz, and “I’m stuck” moment.
- Enrollment Services
- On-Demand Tutors
- Academic Advisors
- Tech Support
Course Professor
Ms. Sayali Deshpande
Passionate math educator, specializing in algebraic reasoning and mathematical foundations for college learners.
Tutoring & Career Resources
Your StraighterLine membership comes with the tools and guidance you need to thrive academically and take confident steps toward your career.
24/7 live, on-demand tutoring, access via chat or video
Exam and certification prep tools
Faculty Connect portal
24/7 live, on-demand tutoring, access via chat or video
Real, human feedback to help you ace your assignments
Exam and certification prep tools
Real, human feedback to help you ace your assignments
Professional development assistance
Resume-building resources
Professional development assistance
Faculty Connect portal
Resume-building resources
Students who enrolled also took:
TRY FOR FREE
Start Your Free Preview
Explore course content, your Student Dashboard, and all the features StraighterLine offers to support your success. No credit card, no commitment — see how easy it is to use StraighterLine.
Get Started FreeStudent Reviews
4.6
You Guys Cut Right to the Chase
You guys cut right to the chase. No rigamarole. Just informative calculus videos. Thanks a lot.
Joshua, StraighterLine Student
Enabled me to complete my degree so much sooner.
Enabled me to complete my degree so much sooner. Immensely valuable and highly efficient!
My husband wishes StraighterLine were available sooner so he could have leveraged the service. What a game changer for continuing ed/lifelong learning.
Tracey, StraighterLine Student
I had a GREAT experience using StraighterLine
I had a GREAT experience using StraighterLine. All of my credits (78) transferred to my university, and cut my time in school in half. The classes were structured well, allowing for an accelerated or slower pace, and the platform is user-friendly. I loved my experience!
Jasmine, StraighterLine Student
Getting Started is Simple
The StraighterLine Advantage
Full flexibility, no timelines or deadlines ever.
Your own support team to get you to the finish line.
Unlimited course access so you can take as many courses as you need.
Transfer guaranteed to one of our 180+ partner schools, and accepted by 3,000+ schools nationwide.
How to Enroll in Calculus II
Select your course and click “Enroll Today”.
Create your account and finalize course purchase.
Start earning affordable college credits!
You’ve Got Questions, We’ve Got Answers
Why is StraighterLine so affordable?
StraighterLine offers a completely online learning experience, free from the high costs of traditional colleges and universities. By cutting out the institutional overhead, we pass the savings onto you (instead of extra costs) — providing top-quality courses at a price that fits with your budget
What is included in the price?
StraighterLine membership gives you access to over 75 self-paced online courses at a fraction of the price you’d pay through your school — meaning you’ll save up to 90% per course. But that’s not all — membership also comes with valuable extras at no extra cost, including academic advising, 24/7 on-demand tutoring, and free transcript delivery to your school
What is ACE, and why does it matter for transfer credits?
StraighterLine courses are recommended for college credit by the American Council on Education (ACE), a respected organization that helps colleges evaluate nontraditional learning for credit. If your school accepts ACE Credit recommendations, there’s a strong chance they’ll accept StraighterLine courses. Always check with your school’s registrar to confirm how transfer credits apply to your degree.
How do I transfer StraighterLine credit?
Transferring your StraighterLine credits is easy:
- Check with your school: If you’re enrolled at one of our 180+ partner colleges, your credits are guaranteed to transfer based on which of our courses your school has agreed to directly accept credit for. Plus, StraighterLine credits have also been accepted by over 3,000 colleges and universities, but it’s always a good idea to confirm your school’s transfer policies before enrolling in a course.
- Request your transcript: Once you complete a course with a 70% or higher, log into your StraighterLine account to request an official transcript. We’ll send it directly to your school at no extra cost.
- Apply your credit: Your school will review your transcript and apply eligibility credits toward your degree, helping you move forward on your academic journey.
Helpful Resources
SUPPORT
Need Help Enrolling?
Our Enrollment Specialists are here to help you get started.
BLOG ARTICLE
How Do StraighterLine Online Courses Work?
Find out what your online learning experience with StraighterLine will be like.
BLOG ARTICLE
Where Can You Transfer StraighterLine Credit?
An easy-to-understand guide on how to transfer StraighterLine credits.
BLOG ARTICLE
How StraighterLine Reduces Tuition Costs
See how StraighterLine has helped students save thousands on tuition.
Calculus II: A Strong Start to Your STEM Career
Calculus II helps you deepen your understanding of change and accumulation. It’s where techniques, theory, and applications come together, preparing you for higher-level math and physics. Whether you go on to become a data scientist, actuary, software developer, or financial manager, calculus teaches you the skills you’ll need to be successful in your career.
Why it matters:
- New jobs for mathematicians and statisticians are projected to grow 11% between 2023–2032 — that’s 3× higher than the average.
- Calculus II guides you into more advanced techniques in mathematics.
How this course sets you up for success:
Data Scientist, Actuary, Statistician, Operations Research Analyst, Quantitative Analyst, Mathematical Modeler, Cryptographer, Financial Analyst, Market Research Analyst, Software Engineer
How this course sets you up for success:
Calculus II teaches you skills you’ll need for engineering, physics, computer science, and data analysis. You’ll deepen your analytical skills and take a major step toward more advanced STEM courses and careers.
Course included in Semester & Annual Plans
SCRIPT HERE DO NOT DELETE