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$$ \int_0^{1} \int_0^{\sqrt{1+x^2}} \frac{1}{\sqrt{x^2 + y^2}}\, dy dx $$

The question need to be solved using double integrals concept. I think the curve is rectangular hyperbola.

user766319
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1 Answers1

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The region of integration is the portion of the unit circle lying in the first quadrant. Now convert into polar form. Then your integral is $\int_{0}^{\pi/2}\int_{0}^{1}(1/r)rdrd\theta=\int_{0}^{\pi/2}(\int_{0}^{1}dr)d\theta=\pi/2.$

user159888
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  • $$ \int_0^{1} \int_0^{\sqrt{1+x^2}} \frac{1}{\sqrt{x^2 + y^2}}, dy dx $$ I have edited the question.Please try now – user766319 Apr 01 '20 at 11:25