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

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Homework Help Overview

The discussion revolves around a double integral involving the square root of the expression 1-x^3, which the original poster is struggling to solve. The context is within a Calculus II course, focusing on integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster mentions using integration by parts and substitution methods for difficult integrals. Some participants provide hints related to derivatives, while others question the validity of the original poster's results, particularly regarding the possibility of obtaining zero as an answer.

Discussion Status

The discussion is ongoing, with hints being offered to guide the original poster. There are indications of confusion regarding the results obtained, and participants are exploring the implications of the integral's properties.

Contextual Notes

Participants are discussing assumptions about the behavior of the integral, particularly at specific values of x, and how these assumptions may affect the results. There is also a mention of the original poster's final answer and its implications.

Alexstrasza
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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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Likes   Reactions: Chestermiller
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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