   Chapter 8.4, Problem 51E

Chapter
Section
Textbook Problem

# True or False? In Exercises 47-50, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If x = sin θ , then ∫ d x 1 − x 2 = ∫ d θ

To determine
Whether the statement “If x=sinθ, then dx1x2=dθ” is true or false. Explain if the statement is false.

Explanation

The integral is;

dx1x2

Put x=sinθ in the above integral.

Differentiate both sides of x=sinθ with respect to θ to get;

dx=cosθdθ

So, the above indefinite integral can be written as;

dx1x2=

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