Change the cartesian integral int_{-1}^{1} int_{0}^{sqrt{1-x^{2}}} (sqrt{x^{2} + y^{2}})dydx into equivalent polar integral and then after evaluating the polar integral the answer is pi .A 2pi .B frac{2pi}{3} .C D. None of these answers frac{pi}{3} .E
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To do this, we need to express the limits of integration in terms of polar coordinates. The limits of integration for y are from 0 to sqrt(r^2-x^2), and the limits of integration for x are from -sqrt(r^2-y^2) to sqrt(r^2-y^2). Using the trigonometric identity Show more…
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