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Question

Area bounded by the curve y=xex2 x - axis and the ordinates x = 0, x = a


A
ea2+12 sq.unit
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B
ea212 sq.unit
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C
ea2+1 sq.unit
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D
ea21 sq.unit
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Solution

The correct option is B ea212 sq.unit
Required area is a0y dx=a0xe x2 dx
We put x2=t dx=dt2x as x=0t=0 and
x=at=a2, then it reduces to
12a20et dt=12[et]a20=ea212sq. unit

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