For the life of me I can't solve this integral sqrt(1-x^3)

[Alexstrasza]

Homework Statement

Hi, I have a double integral with square root of 1-x^3 that I can't solve.

Here is the integral and attempt at the solution. I get stuck!

Homework Equations

I am in Calc II.

Mostly we used integration by parts, or substituting t=something for most "difficult" integrals.

The Attempt at a Solution

Above.

Hope someone can help or give me a hint how to solve this.

Thanks!

 

[mfb]

Hint: x² is the derivative of 1-x³ (up to a prefactor).

 

[Alexstrasza]

Hint: x² is the derivative of 1-x³ (up to a prefactor).

Thank you!

I solved it and got 0 for an answer, is that possible?

 

[mfb]

$\sqrt{1-x^3}$ is positive everywhere, can the result be 0?

 

[Alexstrasza]

Oops, when I solved for x=1 I got 0 and for some reason assumed solving for x=0 would also be 0.

I got 2/9 final answer.

Thank you for helping. :)