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Question: Let I<sub>1</sub>= \(\int _ { 0 } ^ { 1 } 2 ^ { x ^ { 2 } } d x\) , I<sub>2</sub> = \(\int _ { 0 }...

Let I1= ∫012x2dx\int _ { 0 } ^ { 1 } 2 ^ { x ^ { 2 } } d x , I2 = ∫012x3dx\int _ { 0 } ^ { 1 } 2 ^ { \mathrm { x } ^ { 3 } } d x . Then

A

I1 = I2

B

I1< I2

C

I1> I2

D

None of these

Answer

I1> I2

Explanation

Solution

As 0 < x < 1

Ž x2> x3

Ž >

Ž ∫012x2\int _ { 0 } ^ { 1 } 2 ^ { \mathrm { x } ^ { 2 } } dx > ∫012x3\int _ { 0 } ^ { 1 } 2 ^ { \mathrm { x } ^ { 3 } } dx Ž I1 > I2