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

Lix Lemjay | Certified Educator

calendarEducator since 2012

starTop subjects are Math and Science

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`

-----------------------------

`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...

(The entire section contains 266 words.)