Integration of Cosine Cubed Function

The video tutorial demonstrates how to integrate cosine cubed of X using u-substitution. It begins by modifying the expression with trigonometric identities, specifically replacing cosine squared with 1 minus sine squared. The tutorial then applies u-substitution by setting u equal to sine X, simplifying the integral. The antiderivative is calculated, and variables are replaced to present the final solution: sine X minus one-third sine cubed X plus C.

What is the first step in solving the integral of cosine cubed of X?

• Performing u-substitution

• Differentiation

• Direct integration

• Using trigonometric identities

Tags

CCSS.HSF.TF.C.8

How can cosine squared be expressed using the Pythagorean identity?

• 1 + cosine squared

• 1 + sine squared

• 1 - sine squared

• sine squared - 1

What substitution is made for u in the integration process?

• u = cosine X

• u = tangent X

• u = secant X

• u = sine X

What is the derivative of sine X with respect to X?

• negative sine X

• negative cosine X

• cosine X

• sine X

What is the antiderivative of 1 with respect to u?

• u squared

• u cubed

• u

• 1/u

What is the antiderivative of u squared with respect to u?

• u squared

• u to the fourth over 4

• u cubed over 3

• u squared over 2

What is the final expression for the integral of cosine cubed of X?

• cosine X minus 1/3 cosine cubed X plus C

• cosine X plus 1/3 cosine cubed X plus C

• sine X minus 1/3 sine cubed X plus C

• sine X plus 1/3 sine cubed X plus C