Question

${\int }_0^{\pi /2}\sin xdx$ is equal to ?

• A. $\frac{\pi }{8}(1+\sqrt{2})$
• B. $\frac{\pi }{4}(1+\sqrt{2})$
• C. $\frac{\pi }{8\sqrt{2}}$
• D. $\frac{\pi }{4\sqrt{2}}$

Answer 1

The correct option is A $\frac{\pi }{8}(1+\sqrt{2})$

${\int }_0^{\frac{\pi }{2}}\sin xdx\Rightarrow \frac{\frac{\pi }{2}-0}{4}(\sin 0+\sin \frac{\pi }{2}+2\sin \left(\frac{0+\frac{\pi }{2}}{2}\right))\Rightarrow \frac{\pi }{8}(0+1+2\sin 45)\Rightarrow \frac{\pi }{8}(1+2\times \frac{1}{\sqrt{2}})\Rightarrow \frac{\pi }{8}(1+\sqrt{2})$