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Question

The area enclosed by the curve x=y2+2, ordinates y = 0 & y = 3 and the Y - axis is sq. units.

A
5
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B
10
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C
15
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Solution

The correct option is C 15
We have seen that if g(y)0 for yϵ [c, d] then the area bounded by curve x = g(y) and y-axis between abscissa y = c and y = d is dcg(y)dy .
We'll use the same concept here. Here the curve given is
x=y2+2 and c = 0 &d=3.So,g(y)0 x(0,3)
Let the area enclosed be A.
A=30(y2+2)dy.
A=(y33+2y)|30A=9+60A=15

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