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Question

Let I1=10ex2dx,I2=10excos2xdx and I3=10ex2cos2xdx. Then

A
I1<I2<I3
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B
I3<I2<I1
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C
I2<I1<I3
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D
I2<I3<I1
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Solution

The correct option is D I2<I3<I1
When 0<x<1
x2<xex2<exex2>ex
Multiply both sides by cos2x we get
ex2cos2x>excos2x10ex2cos2xdx>10excos2xdxI3>I2
Similarly since 0<cos2x<1
1ex2>cos2xex2I1>I3I2<I3<I1

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