Find area under the curve? Pl refer to the question in the img attached

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1 Answer
Dec 24, 2017

A=49

Explanation:

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This is a piece-wise function. We have to find the area under each piece separately and add them up.

y=-1

The area under this piece from -2 to 0 is:

A_1=int_-2^0 -dx=-x=-(0)-(-(-2))=0-2=-2

y=(x+2)^2

The area under this piece from 0 to 3 is:

A_2=int_0^3(x+2)^2dx

Let u=x+2, then du=dx

A_2=intu^2du=1/3u^3=1/3(x+2)^3=1/3(3+2)^3-1/3(0+2)^3

A_2=125/3-8/3=117/3=39

y=x

The area under the curve for this piece from 3 to 5 is:

A_3=int_3^5xdx=1/2x^2=1/2(5)^2-1/2(3)^2=25/2-9/2=16/2=8

Area under the piece-wise function is:

A=A_1+A_2+A_3=2+39+8=49