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Question

If I is the greatest of the definite integrals
I1=10excos2x dx, I2=10ex2cos2 x dx
I3=10ex2dx, I4=10ex22dx, then


A

I=I1

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B

I=I2

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C

I=I3

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D

I=I4

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Solution

The correct option is D

I=I4


For 0 < x < 1, we have 12x2<x2<x
x2>x, so that ex2<ex,
Hence 10ex2 cos2 x dx>10excos2x dx
Also cos2 x 1
Therefore 10ex2cos2 x dx10ex2dx<10ex22dx=I4
Hence I4 is the greatest integral

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