This is a large collection of practice problems, solutions and references on Integral Calculus. The material here was created by instructors at various universities and colleges for their introductory calculus courses. It takes the form of worksheets, homework, and quizzes, with solutions provided in all cases. We’ve also included some good quality free video and text references.
We also have a collection on Differential Calculus. If you’re self studying calculus, we recommend beginning by watching a series of lecture videos listed under the “Good Viewing” tab below. Once you’ve watched a particular video, try some relevant problems, and then look through the solutions. We think this is an effective way to master the subject. Please write to us at info@tutorterrace.com with any questions, suggestions or comments!
This is an accessible series of lecture videos on Integral Calculus by Prof Komarova of UC Irvine.
This is a complete series of lecture videos from a great introductory Calculus course by Prof David Jerison of MIT.
This excellent video by Prof Strang of MIT gives a “big picture” explanation of integrals.
This highly recommended series of 12 videos by 3Blue1Brown discusses the “essence of calculus”.
This concise yet clear introduction to Integral Calculus from OpenStax is edited by Professors Gilbert Strang and Edwin Herman. It covers the basics of integration, various integration techniques, as well as differential equations and sequences and series. It is suitable for both high school and college students learning calculus.
This classic textbook by Professor Gilbert Strang of MIT is a thorough introduction to Calculus and its applications. There is also an accompanying Study Guide which has model problems and solutions.
Anti-Derivatives and Applications
Worksheet 1, Solutions; Worksheet 2, Solutions (Prof Buehler, UC Berkeley) || Worksheet 1, Solutions; Worksheet 2, Solutions (R Zhao, UC Berkeley) || Worksheet 1, Solutions, Worksheet 2, Solutions (R Fernando, UC Berkeley) || Worksheet, Solutions (Prof Jerison, MIT) || Worksheet, Solutions (Prof Reinholz, UC Berkeley)
Definite Integral (Riemann Sums)
Worksheet and Solutions (Prof Kouba, UC Davis) || Homework (see Page 4), Solutions (Prof Knill, Harvard) || Worksheet 1, Solutions; Worksheet 2, Solutions (Prof Buehler, UC Berkeley) || Worksheet, Solutions (R Zhao, UC Berkeley) || Worksheet, Solutions (see Page 3) (Prof Jerison, MIT) || Quiz, Solutions (Prof Boas, Texas A&M University) || Worksheet, Solutions (R Fernando, UC Berkeley)
Fundamental Theorem of Calculus
Worksheet, Solutions (Prof Buehler, UC Berkeley) || Homework, Solutions (Prof Reinholz, UC Berkeley) || Homework (see Page 4), Solutions (Prof Knill, Harvard) || Worksheet (see Page 2), Solutions (Page 5) (Prof Jerison, MIT) || Worksheet 1, Solutions; Worksheet 2, Solutions (R Zhao, UC Berkeley) || Worksheet, Solutions (Prof Jiang, University of Michigan)
Techniques for Computing Integrals
[Substitution] Worksheet1 and Solutions; Worksheet 2 and Solutions; Worksheet 3 and Solutions (Prof Kouba, UC Davis) || Worksheet, Solutions (Prof Buehler, UC Berkeley) || Homework (see Page 4), Solutions (Prof Knill, Harvard) || Worksheet (see Page 2), Solutions (see Page 5) (Prof Jerison, MIT) || Homework, Solutions (Prof Reinholz, UC Berkeley) || Worksheet, Solutions (R Zhao, UC Berkeley) || Worksheet, Solutions (R Fernando, UC Berkeley) [Trig Substitution] Worksheet and Solutions (Prof Kouba, UC Davis) || Homework (see Page 4), Solutions (Prof Knill, Harvard) [Partial Fractions] Worksheet and Solutions (Prof Kouba, UC Davis) || Homework (see Page 4), Solutions (Prof Knill, Harvard) || Worksheet (see Page 4), Solutions (Page 12) (Prof Jerison, MIT) [Integration by Parts] Worksheet and Solutions (Prof Kouba, UC Davis) || Homework (see Page 4), Solutions (Prof Knill, Harvard) || Worksheet (see Page 5), Solutions (Page 17) (Prof Jerison, MIT) || Worksheet, Solutions (Prof Jiang, University of Michigan)
Using Integrals to Compute Areas and Volumes
[Areas] Worksheet and Solutions (Prof Kouba, UC Davis) || Homework, Solutions (Prof Reinholz, UC Berkeley) || Homework (see Page 4), Solutions (Prof Knill, Harvard) || Worksheet, Solutions (Prof Jerison, MIT), Worksheet, Solutions (R Fernando, UC Berkeley) || Worksheet, Solutions (Prof JIang, University of Michigan) [Volumes] Worksheet, Solutions (Prof Buehler, UC Berkeley) || Worksheet 1 and Solutions, Worksheet 2 and Solutions (Prof Kouba, UC Davis) || Homework 1, Solutions; Homework 2, Solutions (Prof Reinholz, UC Berkeley) || Homework (see Page 3), Solutions (Prof Knill, Harvard) || Worksheet, Solutions (see Page 3) (Prof Jerison, MIT) || Worksheet, Solutions (Prof JIang, University of Michigan) || Worksheet, Solutions (R Fernando, UC Berkeley)
