Question

∫¹∫²(x) = cotx + sinx dx

Answer 1

Given,

$\int_1 ^2 ( cot x + sin x) dx$

$$= \int_1 ^2 cot x dx + \int_1 ^2 sin x dx$$

$$= [ \space ln|sin x| \space ]_1 ^2 - [cos x]_1 ^2$$

$$= ln |sin2 | - ln |sin 1| - ( cos 2 - cos 1)$$

$$= ln |sin2 | - ln |sin 1| - cos 2 + cos 1$$