Question-181857

Question Number 181857 by KINMATICS last updated on 01/Dec/22

Answered by hmr last updated on 01/Dec/22

\int_{\frac{π}{4}}^{\frac{π}{2}} \int_{0}^{\sqrt{2}} \frac{r c o s (θ)}{r^{2}} r d r d θ

= \int_{\frac{π}{4}}^{\frac{π}{2}} \int_{0}^{\sqrt{2}} c o s (θ) d r d θ

= \int_{\frac{π}{4}}^{\frac{π}{2}} {[r c o s (θ)]}_{0}^{\sqrt{2}} d θ

= \int_{\frac{π}{4}}^{\frac{π}{2}} \sqrt{2} c o s (θ) d θ

= \sqrt{2} {[s i n (θ)]}_{\frac{π}{4}}^{\frac{π}{2}}

= \sqrt{2} (1 - \frac{\sqrt{2}}{2})

= \sqrt{2} - 1

Facebook Tweet Pin