Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$$ \int_{-\sqrt{\vphantom{\large A}2\,}\,}^{\sqrt{\vphantom{\large A}2\,}\,} x\sqrt{4 - x^{4}}\,{\rm d}x $$ I find the answer $0$ by substitution $x^{2} = u$, but it didn't make sense.

share|cite|improve this question
up vote 12 down vote accepted

No substitution is needed. The integrand is an odd function of $x$ and you are integrating on an interval that is symmetric about $0$. Therefore the integral is $0$.

share|cite|improve this answer

make sense with this substitution x=2 sin a

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.