Sketch the region enclosed by the given curves. y = 4 cos 2x, y = 4 − 4 cos 2x, 0 ≤ x ≤ π/2   Find its area.

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You need to find the points of intersection of curves, hence you should solve the equation `4 cos 2x = 4 - 4 cos 2x`  such that:

`4 cos 2x = 4 - 4 cos 2x`

`8 cos 2x = 4 =gt 2 cos 2x = 1 =gt cos 2x = 1/2`

`2x = pi/3, 2pi/3, 4pi/3,...`

Notice that the values `2pi/3, 4pi/3,...`  fall outside the interval `[0,pi/2], ` hence, the limits of integration are 0 and `pi/3` .

You need to select a value for x in interval `[0,pi/3]` ...

(The entire section contains 213 words.)

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