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Become a Calculus 2 Master

Learn everything from Calculus 2, then test your knowledge with 830+ practice questions

Created byKrista King

Last updated 6/2026

English

What you'll learn

Integrals, including approximating area, the dreaded Fundamental Theorem of Calculus, and every kind of integration technique
Applications of Integrals, including volume of revolution with disks, washers and shells, and all kinds of real world applications
Polar & Parametric, including how to sketch polar curves and find the area bounded by polar curves
Sequences & Series, including all the convergence tests, and Taylor and Maclaurin series

Course content

36 sections • 370 lectures • 26h 29m total length

What we'll learn in this course4:18
How to get the most out of this course1:26
Download the formula sheet0:19
The EVERYTHING download0:24

Introduction to indefinite integrals0:21
Indefinite integrals
Indefinite integrals9:04
Explore indefinite integrals and antiderivatives, including constant of integration and dx notation. Learn to integrate polynomials term by term, pull out constants, and apply linearity to split integrals.
Indefinite integrals
Computing indefinite integrals
Computing indefinite integrals9:17
Computing indefinite integrals calculus video example.
Computing indefinite integrals
Trigonometric integrals
Course notes for trigonometric integrals.
Trigonometric integrals7:37
Trigonometric integrals calculus video example.
Trigonometric integrals
Initial value problems
Initial value problems10:55
Explore how the constant of integration arises from indefinite integrals and how initial conditions determine the specific constant in an initial value problem, by solving f'(x)=2 and more complex derivatives.
Initial value problems
Find f given f'' or f'''
Find f given f'' or f'''10:36
Find f given f'' or f'''
BONUS! Extra practice problems. :)0:26

Introduction to definite integrals0:20
Summation notation
Summation notation13:40
Summation notation calculus video example.
Summation notation
Riemann sums
Riemann sums14:10
Riemann sums
Over and underestimation
Over and underestimation10:51
Use derivative tests to determine if a function is increasing or decreasing, then apply left or right endpoints and consider midpoint to assess Riemann sum under- or overestimation of area.
Over and underestimation
Converting summation notation to the integral
Converting summation notation to the integral9:00
Converting summation notation to the integral
Definite integrals
Definite integrals7:50
Explore definite integrals by applying bounds a to b to compute the area under a curve, using F(b) minus F(a), and understand area sign relative to the x-axis.
Definite integrals
Properties of integrals
Properties of integrals12:07
Explore the properties of definite integrals, including swapping limits, zero for integral from a to a, pulling out constants, and change of variable to relate area under the curve.
Properties of integrals
Integrating even and odd functions
Integrating even and odd functions10:30
Integrating even and odd functions
Part 1 of the Fundamental Theorem of Calculus
Part 1 of the Fundamental Theorem of Calculus11:40
Part 1 of the Fundamental Theorem of Calculus
Part 2 of the Fundamental Theorem of Calculus
Part 2 of the Fundamental Theorem of Calculus8:45
Part 2 of the Fundamental Theorem of Calculus
Integrating piecewise functions
Integrating piecewise functions13:16
Learn how to integrate piecewise functions by splitting the integral at breakpoints, relate piecewise definitions to absolute value, and apply with concrete examples.
Integrating piecewise functions
Area under or enclosed by the curve
Area under or enclosed by the curve6:19
Area under or enclosed by the curve
Net Change Theorem
Net Change Theorem8:46
Explore the net change theorem by linking a rate of change to its total change through integrals, using velocity, position, and examples like displacement and distance traveled.
Net Change Theorem
BONUS! Extra practice problems. :)0:26

Introduction to approximating area0:20
Limit process to find area
Limit process to find area15:29
Limit process to find area
Midpoint Rule
Midpoint Rule5:03
Use the midpoint rule to approximate area under a curve by using midpoints of subintervals; for f(x)=x^2+4 on [0,3] with n=3, it gives 20.75, close to 21.
Midpoint Rule
Trapezoidal Rule
Trapezoidal Rule6:01
Trapezoidal Rule
Simpson's Rule
Course notes for simpson's rule.
Simpson's Rule5:54
Simpson's rule calculus video example.
Simpson's Rule
Error bounds
Error bounds15:38
Analyze error bounds for the midpoint rule, trapezoidal rule, and Simpson's rule to estimate the maximum error in area under a curve using second and fourth derivatives.
Error bounds
BONUS! Extra practice problems. :)0:26

Introduction to substitution and integration by parts0:21
Substitution
Substitution13:12
Master u-substitution to transform complex integrals into simple polynomials, then back-substitute to obtain clean antiderivatives across exponentials, trig, and rational functions.
Substitution
Substitution in definite integrals
Substitution in definite integrals6:21
Substitution in definite integrals
Integration by parts
Course notes for integration by parts.
Integration by parts12:50
Integration by parts calculus video example.
Integration by parts
Integration by parts with substitution
Integration by parts with substitution7:07
Integration by parts with u-substitution calculus video example.
Integration by parts with substitution
Integration by parts two and three times
Course notes for integration by parts two times.
Integration by parts two and three times10:52
Integration by parts (two times) calculus video example.
Integration by parts two and three times
Tabular integration
Course notes for tabular integration.
Tabular integration7:28
Tabular integration calculus video example.
Tabular integration
BONUS! Extra practice problems. :)0:26

Introduction to trigonometric integrals0:20
Integrating sin^m cos^n
Integrating sin^m cos^n7:38
Integral of sin^m cos^n calculus video example.
Integrating sin^m cos^n
Integrating tan^m sec^n
Integrating tan^m sec^n9:44
Integral of tan^m sec^n calculus video example.
Integrating tan^m sec^n
Integrating products of single sine and cosine factors
Integrating products of single sine and cosine factors6:08
Integrals of the products of single sine and cosine factors calculus video example.
Integrating products of single sine and cosine factors
Hyperbolic integrals
Course notes for hyperbolic trigonometric integrals.
Hyperbolic integrals6:49
Integrals of hyperbolic trig functions calculus video example.
Hyperbolic integrals
Inverse hyperbolic integrals
Course notes for inverse hyperbolic trigonometric integrals.
Inverse hyperbolic integrals5:51
Integrals of inverse hyperbolic trig functions calculus video example.
Inverse hyperbolic integrals
BONUS! Extra practice problems. :)0:26

Introduction to trigonometric substitution0:20
Trigonometric substitution setup
Course notes for trigonometric substitution.
Trigonometric substitution setup13:12
Trigonometric substitution setup calculus video example.
Trigonometric substitution setup
Trigonometric substitution with secant
Trigonometric substitution with secant13:35
Trigonometric substitution with secant
Trigonometric substitution with sine
Trigonometric substitution with sine12:21
Trigonometric substitution with sine calculus video example.
Trigonometric substitution with sine
Trigonometric substitution with tangent
Trigonometric substitution with tangent14:48
Trigonometric substitution with tangent calculus video example.
Trigonometric substitution with tangent
BONUS! Extra practice problems. :)0:26

Introduction to partial fractions0:20
Distinct linear factors
Distinct linear factors12:39
Partial fractions with distinct linear factors calculus video example.
Distinct linear factors
Repeated linear factors
Repeated linear factors12:37
Partial fractions with repeated linear factors calculus video example.
Repeated linear factors
Distinct and repeated quadratic factors
Distinct quadratic factors16:03
Partial fractions with distinct quadratic factors calculus video example.
Repeated quadratic factors14:34
Partial fractions with repeated quadratic factors calculus video example.
Distinct and repeated quadratic factors
Rationalizing substitutions
Course notes for rationalizing substitutions.
Rationalizing substitutions12:29
Rationalizing substitutions for partial fractions calculus video example.
Rationalizing substitutions
BONUS! Extra practice problems. :)0:26

Introduction to improper integrals0:20
Improper integrals, cases 1-3
Improper integrals, cases 1-312:56
Improper integrals, case type 1 calculus video example.
Improper integrals, cases 1-3
Improper integrals, cases 4-6
Improper integrals, cases 4-612:36
Improper integrals, case type 4 calculus video example.
Improper integrals, cases 4-6
Comparison Theorem
Comparison Theorem12:02
Comparison Theorem
BONUS! Extra practice problems. :)0:26

Requirements

You should have a decent foundation (but it doesn't have to be perfect! :D) in Algebra.
If you have some experience with Trigonometry and Precalculus, that will definitely be helpful, but it's not absolutely necessary.
A good foundation in Calculus 1 (limits and derivatives) is required for this course.

Description

HOW BECOME A CALCULUS 2 MASTER IS SET UP TO MAKE COMPLICATED MATH EASY:

This 557-lesson course includes video and text explanations of everything from Calculus 2, and it includes 180 quizzes (with solutions!) and an additional 20 workbooks with extra practice problems, to help you test your understanding along the way. Become a Calculus 2 Master is organized into the following sections:

Integrals
Applications of Integrals
Polar & Parametric
Sequences & Series

AND HERE'S WHAT YOU GET INSIDE OF EVERY SECTION:

Videos: Watch over my shoulder as I solve problems for every single math issue you’ll encounter in class. We start from the beginning... I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.

Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don’t.

Quizzes: When you think you’ve got a good grasp on a topic within a course, you can test your knowledge by taking one of the quizzes. If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.

Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbook. The workbooks include tons of extra practice problems, so they're a great way to solidify what you just learned in that section.

HERE'S WHAT SOME STUDENTS OF BECOME A CALCULUS 2 MASTER HAVE TOLD ME:

“Excellent Quality course. I just finished Calculus 1 and wanted to start learning calculus 2. The instructor gives you quick feedback and is very clear on every example she posts. I highly recommend this course for anyone who wants to learn more about integrals.” - Nick Z.
“This is a superior course. I have taken MOOC Calculus courses now through Ohio State, and MIT (also superior). Krista King is an excellent instructor, with superior knowledge, and nails down precisely what one needs to know, and also provides superior supportive notes.” - Snowcrash
“Krista is saving my butt in my Calc2 class. I always review her videos and do practice problems before my quizzes and exams.” - Nye W.
“Krista's energy and thoroughness make sitting through an explanation simple and motivating. There are loads of examples, with quizzes to check your progress, and detailed explanations on ALL the quiz questions. Plus she answers questions quickly and is very professional! Worth every penny, bought her whole series. It will also help with physics and economics, as she includes relevant explanations and exercises for applications in those topics as well. Got an A in calc 1 online because of her calc 1 course, and now I have gotten an A in calc 2 online as a first time student of it and in a summer semester (shortened!) Thank god I have her calc 3 course, I know I will need it next semester!” - Jennifer L.
“I just can't get over how well she teaches her classes. I have now taken all 3 of her Calculus classes and I really do have a strong understanding of calculus concepts. If only more people could teach the way she does. These concepts that seem so hard she has made easy and clear. My favorite part are the quizzes. She has just enough gotcha's to really get you thinking and remembering concepts. I really just cannot say enough good things about this course and the teacher!” - Morgan G.
“The instructor goes through every little step no matter how minor. It makes learning the material fun! Thank you so much for this wonderful and detailed course!” - Immanuel W.
“This is the second of three courses I have purchased from Krista and she does an incredible job of breaking down the complicated concepts into easy to understand steps. Her courses are very thorough and include a variety of different methods of instruction. Well thought out course. Thank you Krista!!!” - John C.

YOU'LL ALSO GET:

Lifetime access to Become a Calculus 2 Master
Friendly support in the Q&A section
Udemy Certificate of Completion available for download
30-day money back guarantee

Enroll today!

I can't wait for you to get started on mastering calculus 2.

- Krista :)

Who this course is for:

Anyone who's completed Calc 1 and wants to take the next step
Current calculus students, or students about to start Calc 2 who are looking to get ahead
Homeschool parents looking for extra support with calculus
Anyone who wants to study calculus for fun after being away from school for a while

Become a Calculus 2 Master

What you'll learn

Explore related topics

Course content

Getting started4 lectures • 6min

Integrals - Indefinite integrals12 lectures • 48min

Integrals - Definite integrals26 lectures • 2hr 8min

Integrals - Approximating area12 lectures • 49min

Integrals - Substitution and integration by parts14 lectures • 59min

Integrals - Trigonometric integrals12 lectures • 37min

Integrals - Trigonometric substitution10 lectures • 55min

Integrals - Reduction formulas4 lectures • 8min

Integrals - Partial fractions11 lectures • 1hr 9min

Integrals - Improper integrals8 lectures • 38min

Requirements

Description

Who this course is for: