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The value of int1^(e^(37))(pisin(piI nx)...

The value of `int_1^(e^(37))(pisin(piI nx))/xdx` is (a)2 (b) 4 (c) `e^(27)` (d) `e^(37)`

Text Solution

Verified by Experts

The correct Answer is:
2
Let `I= int_(1)^(37pi)(pi sin(pilogx))/(x)dx`
put ` pi log = t`
`rArr (pi)/(x)dx = dt`
` :. I= int _(0)^(37pi)sin(t) dt =- [cos t]_(0)^(37pi)=-[cos37pi-cos0]`
`=- [(-1)-1]=2`
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