Question

Solve

$\underset{\frac{\pi }{4}}{\overset{\frac{\pi }{2}}{\int }}(2\sin x-\cos 5x)dx$

Answer 1

${\int }_{\frac{\pi }{4}}^{\frac{\pi }{2}}(2\sin x-\cos 5x)dx=2[-\cos x{]}_{\frac{\pi }{4}}^{\frac{\pi }{2}}-\frac{1}{5}[\sin 5x{]}_{\pi /4}^{\pi /2}=\sqrt{2}-\frac{1}{5}[1+\frac{1}{\sqrt{2}}]=\frac{9\sqrt{2}-2}{10}$