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Integrals For Calculus 1 and 2
Rating: 5.0 out of 5(6 ratings)
27 students

Integrals For Calculus 1 and 2

Your complete guide for learning all the integral techniques for calculus 1 and calculus 2 course.
Created byLonzo Fulwider
Last updated 6/2025
English

What you'll learn

  • Learn the difference between definite and indefinite integrals.
  • Learn all the basic integration rules.
  • Learn u-substitution method.
  • Learn integration by trigonometric substitution.
  • Learn integration by trigonometric substitution with completing the square.
  • Learn integration by parts more than once and tabular method.
  • Learn integration by parts with: inolving ln(x), more than once, tabular method, definite integrals, and with LIATE.
  • Learn integration powers of sines and cosines.
  • Learn integration powers of tangents and secants.
  • Learn integration with partial fraction including: linear and non repeating quadratic, linear and repeating quadratic, and with imroper rational function.
  • Learn improper integral type 1.

Explore related topics

Course content

2 sections • 43 lectures • 19h 6m total length

  • Riemann Sum Part 130:29

    In this video, I will introduce the Riemann Sum which is basically estimating the area under a curve by making small rectangles finding the area of each rectangles and then adding them up. I'll go over the different techniques of estimating area under the curve such as: right, left, midpoint, and trapezoidal method of riemann sum.

  • Part 2 Of Riemann Sum40:45

    This is part 2 of riemann sum.

  • Part 3 Of Riemann Sum50:47

    This is part 3 of riemann sum.

  • Sigma Notation1:09:03

    In this video, I will introduce sigma notation and limits of finite sums which is basically the formal definition of a Riemann Sum and definite integral. In this video, you will solve limit problems by taking a function and express it as the limit of a sequence of Riemann Sums over an interval.

  • Integration Rules39:56

    In this video, I will go over some common integration rules, and go over the difference between definite and indefinite integral.

  • Integrals and Indefinite Integration21:54

    In this section, I will introduce what is an integral and indefinite integral. Also I will explain how you can get f''(x), f'(x) to regular f(x) with the help of integrals.

  • Integration By U-Subsitution28:00

    In this video, I will introduce u substitution.

  • Integration By U-Substitution (Simple Examples)37:06

    In this video, I will go over integration by u-substitution simple examples.

  • U-Substitution (Medium-Hard Examples)29:05

    In this video, I will integrate using u substitution using medium-hard examples.

  • Example 1 Of Harder Example Of U-Substitution10:52

    In this video, I will do example 1 of a harder example of u-substitution.

  • Ex) 2 U-Substitution Of Harder Example3:36

    I will go over u substitution of harder example.

  • Ex) 3 U-Substitution Of Harder Example6:32

    In this video, I will do example 3 of a harder u-substitution that requires double substitution.

  • Integration By Trigonometric Substitution1:02:24

    In this video, I will go over all the steps for integration by substitution.

  • Ex) 2 Of Integration By Trigonometric Substitution14:43

    In this video, I will do example 2 of integration by trigonometric substitution.

  • Ex) 3 Of Integration By Trigonometric Substitution20:03

    In this video I will do ex)3 of integrating using trigonometric substitution.

  • Ex)4 Of Integration By Trigonometric Substitution16:40

    In this video, I will do example 4 of trigonometric substitution.

  • Ex) 5 Integration By Trigonometric Substitution With Completing The Square13:16

    This is example 5 of integration by trigonometric substitution with completing the square.

  • Ex)6 Of Trigonometric Substitution Integration With Completing The Square17:07

    This is example six of trigonometric substitution integration with completing the square.

  • Quiz: On Integration With Trigonometric Substitution16:21

    In this video I will go over a quiz on integration with trigonometric substitution.

  • Intro To Integration By Parts9:14

    In this video, I will go over integration by parts.

  • Ex) 2 Of Integration By Parts Involving ln(x)4:12

    In this video, I will do example two of integration by parts involving ln(x).

  • Ex) 3 Integration By Parts More Than Once14:08

    This is example 3 of integration by parts more than once.

  • Integration By Parts Tabular Method10:55

    In this video, I will introduce the tabular method for integration by parts.

  • Integration By Parts For Definite Integrals10:03

    In this video, I will do integration by parts with definite integral.

  • Integration By Parts With LIATE9:06

    In this video, I will integrate by parts with the help of LIATE.

  • Quiz On Integration By Parts11:14

    In this video, I will go over the quiz on integration by parts.

  • Integrating Powers Of Sines And Cosines19:45

    In this video, I will go over integrating powers of sines and cosines. This is not integrating with trig substitution.

  • Quiz On Integrating Powers Of Sines And Cosines7:04

    In this video, I will go over the quiz on integrating powers of sines and cosines when both power are odd.

  • Integrating Powers Of Tangents And Secants16:17

    In this video, I will go over how to integrate powers of tangents and secants.

  • Advanced Trigonometric Integration(Powers Of Sine, Cosine, Secant, And Tangent)42:21
  • Part 2 Of Advanced Trigonometric Integration34:25
  • Integration With Partial Fraction19:01

    In this video, I will integrate with partial fraction using two examples with non repeating linear factor, and repeated linear factor.

  • Integration Partial Fraction With Linear And Non Repeating Quadratic25:07

    In this video, I will integrate a partial fraction with a distinct quadratic or higher degree factor.

  • Partial Fraction Integration With Linear And Repeating Quadratic22:54

    In this video, I will integrate partial fraction with linear and repeating quadratic.

  • Partial Fraction Integration With Improper Rational Function And Synthetic Divis11:59

    In this video, I will integrate partial fraction with improper rational function with synthetic division.

  • Quiz On Partial Fraction Integration15:10

    In this video, I will do a quiz on partial fraction integration.

  • Practice Problems For Integration Part 141:30

    This is part 1 of practice problems of integration. These practice problems will require review of: power rule, sum rule, trig integration rule, constant integration rule.

  • Part 2 Of Integration Practice Problems31:29

    This is part 2 of integration practice problems. In these practice problems will require a review of trig identity, and u-substitution.

Requirements

  • High School Level Algebra. Calculus 1 is great, but not required.

Description

This course will go over all the integral techniques for calculus 1 and calculus 2. This course has 8 hours of video lectures, video quizzes, and practice problems pdf form. Each section is ended with a video quiz that you can pause anytime. This course will greatly prepare students who will be taking differential equation, calculus 1, and calculus 2. This course is perfect for anyone who needs a refresher on integral techniques or who will be taking higher level math such as differential equation. After completing this course you should be familiar for integrating any type of integral.


Requirements For This Course:

· High school algebra or algebra 2

· A notebook to write good notes.

· The drive to learn.


Topics That Will Be Covered In This Course:

· Definite and indefinite integrals

· Basic integration rules

· U-substitution method

· Integration by trigonometric substitution

· Integration by trigonometric substitution with completing the square

· Integration by parts more than once and tabular method

· Integration by parts with: involving ln(x), more than once, tabular method, definite integrals, and with LIATE

· Integration powers of sines and cosines

· Integration powers of tangents and secants

· Integration with partial fraction including linear and non-repeating quadratic, linear and repeating quadratic, and with improper rational function

· Improper integral type 1


Who this course is for:

  • Anyone who plans to take any of the following course in the future: calculus 1, calculus 2, and differential equation.

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