Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

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

Let $F(y)=\int_{0}^{y}\sqrt{x^4-(y-y^2)}dx$ for $0 \le y \le 1$. How can one compute the derivative of $F(y)$? I know how to compute such derivative when the integrand is independent of $y$, but I have no idea in this case.

Thank you very much.

share|cite|improve this question

Hint: Write $G(y,z)=\int_0^y\sqrt{x^4-(z-z^2)}$ and note that $F(y)=G(y,z(y))$, where $z(y)=y$.

share|cite|improve this answer

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.