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Integration with trigonometric substitution

Integral Calculus: Master Advanced Integration Techniques

Integrals

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Antiderivatives

Derivatives and Antiderivatives

Derivative and Antiderivative of a Function

Riemann sum

Riemann Sum

Evaluating integrals with a Riemann sum

Evaluating integrals with a Riemann Sum

Riemann Sum with Trapezoid Approximation

Trapezoidal Approximation of Riemann Sums

Fundamental theorem of calculus

Fundamental Theorem of Calculus Part II

Fundamental Theorem of Calculus Part I

Fundamental Theorem of Calculus

Definite integral

Definite Integral

Integration Techniques

Numerical integration

Numerical Integration

U-Substitution

U-Substitution: Integrating Radical Functions

Not-So-Obvious U-Substitution

Trigonometric substitution

Trigonometric Substitution

Integration of rational functions by partial fractions

Improper integrals

Improper Integrals

Integration by parts

Integration using trigonometric identities

Integration Applications

Areas between curves

Volumes of solids of revolution - Disc method

Volumes of solid with known cross-sections

Volumes of solids of revolution - Shell method

Volumes of solid of revolution - Shell method

Arc length

Average value of a function

Introduction to differential equations

Order and solutions to differential equations

Separable equations

Separable Equations

Applications to differential equations

Modeling with differential equations

Slope fields

Understanding Slope Fields

Euler's method

Euler's Method

Euler"s Method

Euler"s method

Sequence and Series

Introduction to sequences

Monotonic and bounded sequences

Introduction to infinite series

Convergence and divergence of normal infinite series

Convergence & divergence of geometric series

Divergence of Geometric Series

Convergence & divergence of telescoping series

Divergence of harmonic series

Divergence of Harmonic Series

P Series

Convergence and Divergence of P Series

Alternating series test

Alternating Series Test

Convergence of the Alternating Series Test

Divergence test

Divergence Test

Comparison & limit comparison test

Comparison & Limit Comparison Test

Integral test

Integral Test for Series Convergence

Convergence/Divergence of Integral Test

Ratio test

Ratio Test

Convergence & Divergence of Ratio Test

Root test

Root Test

Root Test for Series Convergence

Convergence & Divergence of Root test

Absolute & conditional convergence

Absolute & Conditional Convergence

Radius and interval of convergence with power series

Radius of Convergence of Logarithmic Function

Radius and Interval of Convergence with Power Series

Radius of Convergence of Tangent Function

Functions expressed as power series

Taylor series and Maclaurin series

Approximating functions with Taylor polynomials and error bounds

Parametric Equations and Polar Coordinates

Defining curves with parametric equations

Tangent and concavity of parametric equations

Area of parametric equations

Arc length and surface area of parametric equations

Arc Length of a Parametric Curve

Polar coordinates

Tangents of polar curves

Area of polar curves

Arc length of polar curves

Integral calculus made easy!
Get better marks in calculus class with our complete Integral Calculus help. Our calculus tutors cover all topics you will see in any typical Integration class that deals with single variable functions.

Keeping with your textbook and class, our Integral calculus video lessons walk you through all topics in integral calculus such as, Antiderivative, Integral of trig functions, Definite integral, Indefinite integral, Integration by substitution, Improper integrals and more. Learn the concepts with our tutorials that show you step-by-step solutions to even the hardest integral calculus questions. Then, reinforce your understanding with tons of integral calculus practice.
All our lessons are taught by experienced calculus teachers. Let&apos;s finish your homework in no time, and ACE that exam.

Integral Calculus

sample

math

https://dmn92m25mtw4z.cloudfront.net/img_set/textbook-integral-calculus/v1/textbook-integral-calculus-168w.png

Ex 1.

Why trig substitution works using a right triangle approach

Ex 2.

Ex 3.

Integrating 1/(x²√(16−x²)) using trig substitution

Integrating 1/(x²√(x²+9)) using trig substitution

In this section, we will look at evaluating trigonometric functions with trigonometric substitution. A lot of people normally substitute using trig identities, which you will have to memorize. However, Dennis will use a different and easier approach. He will use the idea of Pythagoras Theorem and make a relation with sine and cosine in terms of x to substitute. In more advance questions, we will use Pythagoras Theorem to make a relation with <a href="[[glossary.html|{"keyword":"Tangent (in Trigonometry)"}]]">tangent</a> and secant to substitute. No matter what type of questions you do, you will only need to know Pythagoras Theorem and nothing else!

Combination of SohCahToa questions

Trigonometric substitution

What You'll Learn

Apply the Pythagorean theorem to construct right triangles for trigonometric substitution

Convert radical expressions involving sums and differences of squares into trigonometric functions

Substitute x with trigonometric expressions using sine, tangent, and secant relationships

Evaluate integrals by transforming them from algebraic to trigonometric form

Convert final answers from trigonometric functions back to expressions in terms of x

What You'll Practice

Integrating expressions with square roots of differences of squares using sine substitution

Solving integrals with square roots of sums of squares using tangent and secant substitution

Drawing and applying right triangle relationships to perform substitutions

Simplifying trigonometric expressions and applying u-substitution within trig integrals

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

3 Video lessons

Practice exercises

Learning resources

Skills

Trigonometric Substitution

Integration Techniques

Pythagorean Theorem

Right Triangles

Sine and Cosine

Tangent and Secant

U-Substitution

Calculus