# Solving for a variable integral

## Homework Statement

Find the exact positive value of c if the area between f(x)=x^2-c^2 and the x-axis is equal to 36.

## The Attempt at a Solution

My first step is to take the antiderivative of f(x), giving me F(x)=x^3/3 then applying the fundamental theorem on the interval [-c,c] since that's where the function should cross the x axis.

This gives me 2c^3/3. If I set this equal to 36 I should get the value of c. Solving I get 3*(2)^(1/3) = aprox. 3.78. however if take the integral of x^2-(3.78)^2 on [-3.78,3.78] I get -72 So I'm not sure what I'm doing wrong or where to go from here. Thanks from the help

Mark44
Mentor

## Homework Statement

Find the exact positive value of c if the area between f(x)=x^2-c^2 and the x-axis is equal to 36.

## The Attempt at a Solution

My first step is to take the antiderivative of f(x), giving me F(x)=x^3/3
Stop here. The function is f(x) = x2 - c2, so its antiderivative is not (1/3)x3.
then applying the fundamental theorem on the interval [-c,c] since that's where the function should cross the x axis.

This gives me 2c^3/3. If I set this equal to 36 I should get the value of c. Solving I get 3*(2)^(1/3) = aprox. 3.78. however if take the integral of x^2-(3.78)^2 on [-3.78,3.78] I get -72 So I'm not sure what I'm doing wrong or where to go from here. Thanks from the help

Wow, Thanks for pointing that one out...I figured it out