Find the Integral of (-39240)(9-x^2)^(1/2) with Easy Step-by-Step Guide

Thread starter n05tr4d4177u5
Start date Sep 24, 2005
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Integral

In summary, the first step in finding the integral of (-39240)(9-x^2)^(1/2) is to use the power rule to rewrite the expression. To integrate the expression, you can use the substitution method by letting u = 1-x^2. After using the substitution method, you can use the power rule for integrals to solve for the integral. To use the power rule, add 1 to the exponent and divide by the new exponent. The final step is to substitute back in the original variable, u = 1-x^2, to get the final answer.

Sep 24, 2005

n05tr4d4177u5

Can someone tell me what is the integral of

(-39240)(9-x^2)^(1/2)

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Sep 24, 2005

n05tr4d4177u5

rewritten

-39240 times the square root of (9 - x squared)

Sep 24, 2005

Jameson

Gold Member

MHB

Alrighty. We have [tex]\int -39240\sqrt{9-x^2}dx[/tex]

This is going to use trig substitution. Any ideas?

1. What is the first step in finding the integral of (-39240)(9-x^2)^(1/2)?

The first step is to use the power rule to rewrite the expression as (-39240)(9-x^2)^(1/2) = (-39240)(9)^(1/2)(1-x^2)^(1/2).

2. How do I integrate the expression (-39240)(9-x^2)^(1/2)?

To integrate the expression, use the substitution method by letting u = 1-x^2. This will result in the integral becoming (-39240)(9)^(1/2)∫u^(1/2) du.

3. What is the next step after using the substitution method?

After using the substitution method and rewriting the integral as (-39240)(9)^(1/2)∫u^(1/2) du, you can use the power rule for integrals to solve for the integral.

4. How do I use the power rule for integrals to solve (-39240)(9)^(1/2)∫u^(1/2) du?

To use the power rule, add 1 to the exponent and divide by the new exponent. This will result in (-39240)(9)^(1/2)∫u^(1/2) du = (-39240)(9)^(1/2)((u^(3/2))/(3/2)) + C.