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.

Is there any general way to transform $\int^a_b\int^c_df(x,y)dxdy$ into $\int^k_l\int^m_nf(r,\theta)drd\theta $? If yes, what is it?

I'm a new double integral learner and just have the idea of polar coordinate. Can anyone help me with this Question? Thank you.

share|improve this question

1 Answer 1

up vote 1 down vote accepted

No, if you intend to have constant $a, c, b, d$ and $k, l, m, n$, this is not possible, because in the $xy$ domain you have a rectangle, and its edges have equations, say,

$$ x = A\\ y = B $$

where $A,B$ are constant, and these become in the $r\theta$ domain

$$ r=\frac{A}{\cos\theta}\\ r=\frac{B}{\sin\theta} $$

which cannot be constant, if we exclude the simple case of $A$ or $B$ zero.

share|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.