Question

If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.

Options

• cos x + x sin x + C

• –cos x – x sin x + C

• sin x + x cos x + C

• x sin x – cos x + C

Answer 1

If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = –cos x – x sin x + C.

Explanation:

`π/2` < x < π then

`sqrt((1 + cos 2x)/2)` = |cos x| = – cos x

∴ `intxsqrt((1 + cos2x)/2)dx = –int x cos xdx`

= –[x sin x + cos x] + c