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]` ...
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