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Question

The area bounded by the curve x=at2,y=2at and x-axis is 1t3 is

A
26a2
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B
8a2
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C
26a23
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D
104a23
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Solution

The correct option is D 104a23
Eliminating t, we ontain the equation of the curve as y2=4ax
t=1x=a and t=3x=9a
Hence required area
=9aaydx=9aa2axdx
=2a[x3/23/2]9aa=432[(9a)3/2a3/2]
=43a[27a3/2a3/2]=43a[26a3/2]=1043a2

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