Question

Evaluate the iterated integral by converting to polar coordinates. $$int_{0}^{2} int_{0}^{sqrt{2x-x^2}} 4sqrt{x^2+y^2} , dy , dx$$ $$frac{32}{3}$$

          Evaluate the iterated integral by converting to polar coordinates.
$$int_{0}^{2} int_{0}^{sqrt{2x-x^2}} 4sqrt{x^2+y^2} , dy , dx$$
$$frac{32}{3}$$

$Evaluate the iterated integral by converting to polar coordinates. int0^2 int0^sqrt2x-x^2 4sqrtx^2+y^2 , dy , dx frac323$

Added by Mark E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Alan Ghazarians

01/15/2018

Step 1

Recall that $x = r\cos\theta$, $y = r\sin\theta$, and $dx\,dy = r\,dr\,d\theta$. So, we have: $$\int\int 2x\sqrt{x^2 + y^2}\,dy\,dx = \int\int 2(r\cos\theta)r\,r\,dr\,d\theta$$ Now, we need to find the limits of integration. Since we are not given any specific Show more…

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