Answer to Question #101663 in Calculus for ss

Question

EVALUATE ∫dx/(1+2cosx)

LOWER LIMIT 0
UPPER LIMIT PI/2

Answer 1

$\intop_{0}^{\frac {\pi}2} (1+2cosx)dx= \intop_{0}^{\frac {\pi}2} 1dx +2\intop_{0}^{\frac {\pi}2} cosxdx= (x + 2sinx)\text{\textbar}_0^{\frac{\pi}2}=$

$\frac {\pi}2 +2 sin(\frac {\pi}2) - 0- 2 sin(0) = \frac {\pi}2 +2$