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If int(0)^(1) x e^(x^(2) ) dx=alpha int(...

If `int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx`, hten

A

`alpha in (0,1)`

B

`(1,2)`

C

`(-oo,0)`

D

`(0,oo)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have , `0 lt x lt1`
`:. 0 lt xe^(x^(2)) lt e^(x^(2))`
`rArr underset(0)overset(1)int 0 dxlt underset(0)overset(1)int e^(x^(2)) dx ltunderset(0)overset(1)int e^(x^(2))dx`
`rArr 0 lt alpha underset(0)overset(1)int e^(x^(2)) dxlt underset(0)overset(1)int e^(x^(2)) dx rArr 0 ltalpha lt 1 rArr alpha in (0,1)`
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