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Question

The area enclosed between the curves, x2=y and y2=x is equal to:

A
13 sq. unit
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B
210(xx2)dx
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C
Area enclosed by the region {(x,y):x2yx}
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D
Area enclosed by the region {(x,y):x2yx}
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Solution

The correct options are
A 13 sq. unit
C 210(xx2)dx
D Area enclosed by the region {(x,y):x2yx}
Bothe the curves intersect at
(0,0) and (1,1)
Now,
Area =x=1x=0(y1y2)dx=1x=0(xx2)dx
=x3232x3310=2313=13

Area can also be written as
210(xx2) dx
Due to its symmetry along y=x

Area enclosed by the region
{(x,y)}:x2yx}

Twice the area enclosed by the region
{(x,y)}:x2yx}

Hence, options A, B, and C.

312863_35883_ans.PNG

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