Integrals and Identities of Trigonometric Functions

The video tutorial explains how to find the integral of tangent squared X. It begins by introducing the problem and the need to use a Pythagorean identity. The identity, 1 + tangent squared equals secant squared, is used to rewrite the integral in a simpler form. The tutorial then demonstrates how to solve the integral by finding the antiderivative of secant squared, which is tangent X, and the antiderivative of 1, which is X, plus a constant C. The solution is presented step-by-step, ensuring a clear understanding of the process.

Which identity is used to transform the integral of tangent squared?

• One plus cotangent squared equals cosecant squared

• One plus tangent squared equals secant squared

• Sine squared minus cosine squared equals tangent squared

• Sine squared plus cosine squared equals one

What is the result of subtracting one from secant squared?

• Cosine squared

• Sine squared

• Cotangent squared

• Tangent squared

What is the integral of secant squared?

• Secant X

• Cotangent X

• Cosecant X

• Tangent X

What is the antiderivative of one?

• X squared

• X

• Zero

• One

What is the final result of the integral of tangent squared?

• Tangent X minus X plus C

• Secant X minus X plus C

• Tangent X plus X plus C

• Secant X plus X plus C