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Find the area of the following region y=sin x and y=sin 2x from x=0  x=pi/2

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The formula for area between two curves is:

`A = int_a^b (y_U - y_L) dx`

The integral limits a and b are the intersection points of the two equation. To determine, use elimination method of system of equations.

Subtract the two equations to eliminate y variable.

         `y = sin x`

 `(-) `    `y = sin 2x`

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        `0 = sin x - sin 2x`

To simplify, replace sin 2x with 2sinx cos x. Note that from double angle identity sin 2x = 2sin x cos x .

     ` 0 = sinx - 2sinx cosx`

      `0 = sin x (1-2cos x)`

 Then, set each...

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