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Question

Find the interval in which
f(x)=x1(et1)(2t)dt, (x>1) is
increasing

A
[3,5]
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B
[1,3]
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C
[0,3]
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D
[0,2]
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Solution

The correct option is D [0,2]
f(x)=x1(et1)(2t)dt
The function is increasing if
f(x)>0
By Lebinitz's theoram
f(x)=(ex1)(2x)
We see that f(x)>0 for x[0,2]
So, f(x)=x1(et1)(2t)dt will be increasing in interval x[0,2]

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