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Question

Using integration find the area of the following region (x,y):|x+2|y20x2.

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Solution

y|x+2|
P,Q,R are points of intersection y=20x2 with y=x+2 & x=0
from graph
P=(2,4)
Q=(0,2)
R=(0,25)
area of shaded region =20(20x2(x+2)0dx
=2020x2dx20(x+2)dx
=[x220x2+10sin1x25]20[x22+2x]20
=4+10sin1(15)6
Area =10sin1(15)2

1340153_1083071_ans_700b400738694ce2b43e3ca0231fa52a.png

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