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Question

Find the area enclosed between the curve y=5x−x2 and y=x .


A

16

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B

32

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C

323

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D

329

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Solution

The correct option is C

323


Let’s have a look at the graph of both the functions.

We can see that both the function intersect each other at points (0,0) and (4,4). And the area enclosed will be the area between these points.
Let the area enclosed be A.
A=40(5xx2)x dx
Since, throughout the interval [0,4],5xx2x
So we don’t have to split the integral.
A=404xx2 dxA=(2x2x33)40A=32643A=323


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