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L e tI1=thetaint0^1(e^xdx)/(1+x)a n dI2t...

`L e tI_1=thetaint_0^1(e^xdx)/(1+x)a n dI_2thetaint_0^1(x^2dx)/(e^x^3(2-x^3))dott e h n(I_1)/(I_2)i se q u a lto` `3/e` (b) `e/3` (c) `3e` (d) `1/(3e)`

A

`3//e`

B

`e//3`

C

`3e`

D

`1//3e`

Text Solution

Verified by Experts

The correct Answer is:
C
`I_(1)=int_(0)^(1)(e^(x)dx)/(1+x), I_(2)=int_(0)^(1)(x^(2)dx)/(e^(x^(2))(2-x^(3)))`
In `I_(2)` put `1-x^(3)=t`
`:. I_(2)=1/3 int_(1)^(0) (-dt)/(e^(1-t)(1+t))=1/(3e)int_(0)^(1)(e^(t)dt)/(1+t)=1/(3e)I_(1)`
`:. (I_(1))/(I_(2))=3e`
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