Take the 2-minute tour ×
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.

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

share|improve this question
add comment

2 Answers 2

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|improve this answer
add comment

make sense with this substitution x=2 sin a

share|improve this answer
add comment

Your Answer


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.