Question
Asked Nov 27, 2019
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problem in photo attached

Find the area of the region between the curves y sin(x), y = sin(2x), x = 0, and X
= T/2
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Find the area of the region between the curves y sin(x), y = sin(2x), x = 0, and X = T/2

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Expert Answer

Step 1

Consider the given functions:

f(x)sin
8(x) sin (2x)
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f(x)sin 8(x) sin (2x)

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Step 2

To calculate the area under the curve, the following method is employed:

g(x)>f(x), 0<x<-
g(x)f(x)
Area under the curve is as follows
4-g(x)-f(x
A2-x)-g(x)x
A A A
sin 2x-sinxdx
sin 2xdx-sin xdx
cos 2x
-(-cosx
2T
COS
3
Cos-
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g(x)>f(x), 0<x<- g(x)f(x) Area under the curve is as follows 4-g(x)-f(x A2-x)-g(x)x A A A sin 2x-sinxdx sin 2xdx-sin xdx cos 2x -(-cosx 2T COS 3 Cos-

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Step 3

Further,...

4
4-1
42-f(x)-g(x)x
A2sinxdx sin 2xd
=
4-(-013
cos2x
A2(cosx
2
cos
3
4-{(rc3-(-cn3)}-
COS T
A2
-cos
2.
2
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4 4-1 42-f(x)-g(x)x A2sinxdx sin 2xd = 4-(-013 cos2x A2(cosx 2 cos 3 4-{(rc3-(-cn3)}- COS T A2 -cos 2. 2

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Tagged in

Math

Calculus

Integration