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

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SUMMARY

The discussion centers on solving the double integral of the function √(1-x³) within the context of Calculus II. The user initially struggled with the integral but received hints regarding the derivative of 1-x³, which led to a breakthrough. Ultimately, the user confirmed that the final answer to the integral is 2/9, clarifying that the integral can yield a non-zero result despite initial confusion about the value at specific points.

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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!
 
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Hint: x2 is the derivative of 1-x3 (up to a prefactor).
 
mfb said:
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?
 
##\sqrt{1-x^3}## is positive everywhere, can the result be 0?
 
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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. :)
 

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