   Chapter 4.5, Problem 7E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral. ∫ x 1 − x 2 d x

To determine

To evaluate:

The indefinite integral x1-x2 dx

Explanation

1) Concept:

i) The substitution rule

If u=g(x) is a differentiable function whose range is an interval I and f is continuous on I, then f(gx)g'xdx=f(u)du.

ii) Indefinite integral

xn dx=xn+1n+1+C   (n-1)

2) Given:

x1-x2 dx

3) Calculation:

Here, use the substitution method because the differential of the function 1-x2 is -2xdx

Substitute u=1-x2

Differentiate u=1-x2 with respect to x

du=-2xdx

As x dx is a part of the integration, solving for x dx by dividing both side by 2.

-du2=xdx

By using concept i),

substitute u=1-x2,  xdx=-du2

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