Learn how to find the derivative of the integral

The video tutorial covers the process of integrating a function, specifically focusing on the sine function from X^2 to π/2. It emphasizes the importance of understanding the fundamental theorem of calculus and the application of the chain rule when dealing with functions within functions. The tutorial concludes with deriving the final answer using the cosine function.

What is the integral of sine from X^2 to π/2?

• sine of X^2 minus sine of π/2

• cosine of X^2 plus cosine of π/2

• sine of π/2 minus sine of X^2

• cosine of π/2 minus cosine of X^2

What does the fundamental theorem of calculus allow us to do with integrals?

• Differentiate the integrals directly

• Change the variable of integration

• Rewrite the integrals

• Ignore the upper bound

Why is it necessary to apply the chain rule when the upper bound is a function like X^2?

• Because there is a function within a function

• Because the function is constant

• Because the function is linear

• Because the function is undefined

What is the derivative of the integral when the upper bound is X^2?

• cosine of X times 2X

• sine of X times X

• sine of X times 2X

• cosine of X times X

What is the final answer after applying the chain rule?

• Cosine of X

• Sine of X

• Two times the sine of X

• Two times the cosine of X