   Chapter 4.3, Problem 81E

Chapter
Section
Textbook Problem

# The following exercises are intended only for those who have already covered Chapter 6.Evaluate the integral. ∫ 1 / 2 1 / 2 4 1 − x 2   d x

To determine

To evaluate:

1/21/241-x2 dx

Explanation

1) Concept:

The Fundamental Theorem of Calculus: Suppose f is continuous on [a, b], then

abfxdx=Fb-F(a), where F is antiderivative of f, that is F'=f.

2) Formula:

d/dx (sin-1x)=11-x2

3) Calculations:

Consider

1/21/241-x2 dx

Applying the formula in the above equation ant derivative of 11-x2 is (sin-1x).

Thus using the Fundamental theorem of Calculus

1/21/241-x2 dx=4sin

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