CPM Homework Help : CALC Problem 9-43

Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy. After evaluating each integral, write a short description of your method. Homework Help ✎

Step 1:

$=\int_0^1\frac{1}{\sqrt{1-x^2}}dx+\int_0^1\frac{x}{\sqrt{1-x^2}}dx$

Step 2:

You should have the first integral committed to memory.
For the second integral, let u = 1 − x².

Hint:

This is an improper integral because the graph has a vertical asymptote at x = 0. Rewrite this integral using limits and two separate integrals before evaluating.

Step:

$=\int_0^1\Big(\frac{1}{x}-1\Big)dx$

Hint:

Rewrite the integrand using exponents. This is also an improper integral.