Question

Determine e marque a única resposta correta para a solução da integral: I=∫0π2(1+cos(2ω)2)dω.


A)I=-π4


B)I=π4

C)I=-π4


D)I=π4


E)I=π2

Answer 1

$\displaystyle \int \limits^\frac{\pi}{2} _0 {1+2\cos(2w)} \, dw \\ \\ \\ w+2 \cdot \frac{1}{2} \sin(2w) \\ \\ \\ w+ \sin(2w) + k \\ \\ \\ \displaystyle \int\limits^b_a {f(x)} \, dx = F(b)-F(a) \\ \\ \\ \displaystyle [\frac{\pi}{2} + \sin(2 \cdot \frac{\pi}{2} )]-[0+ \sin(2 \cdot 0)] \\ \\ \\ \boxed{ \frac{\pi}{2} \, \, u.a}$