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Question

The area (in sq. units) of the region (x,y):x0,x+y3,x24yandy1+x is:


A

32

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B

73

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C

52

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D

5912

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Solution

The correct option is C

52


Explanation for correct answer:

Determining the area:

We have a region (x,y):x0,x+y3,x24yandy1+x

The graph of the given curves is shown in the figure.

The area of a shaded region is given below.

A=011+xdx+123-xdx-02x24dxA=x+x323201+3x-x2212-x31202=1+23-0+6-2-3+12-812-0=53+32-812=20+18-812=3012=52

Therefore the area of the shaded portion is equal to 52squareunits

Hence, the correct answer is option (C).


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