Question

HELP!!! Find the area bounded by the curves y = -4sin(x) and y = sin(2x) over the closed interval from 0 to pi.

1.4

2.8

3.16

1/2

none of the above

Answer 1

You need to find the area of the shaded region. For that, you must integrate from 0 to pi/2 a function that takes the function on the top and substracts the one on the bottom. Then you must substract a funcyion that takes the function on the bottom and substracts the function from the top.

\[A=\int\limits_{0}^{\pi}(sen(2x)+4sen(x))dx=-\frac{ 1 }{ 2 }\cos(2\pi)+\frac{ 1 }{ 2 }\cos(0)-4\cos(\pi)+4\cos(0)\]\[A=8\]