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int (1)^(2) (1/x - 1/(2x^(2)))e^(2x) dx ...

` int _(1)^(2) (1/x - 1/(2x^(2)))e^(2x)` dx is equal to

A

`(e^(2))/(2)((e^(2))/(2)-1)`

B

`(e)/(2)((e)/(2)-1)`

C

`(e)/(2)((e^(2))/(2)-1)`

D

`(e^(2))/(2)((e)/(2)+1)`

Text Solution

Verified by Experts

The correct Answer is:
A
` Let l= int_(1)^(2)(1/x-1/(2x^(2)))e^(2x)dx = [ e^(2x).(1)/(2x)] _(1)^(2)`
= ` (e^(4))/4 - (e^(2))/2=(e^(2))/2 (e^(2)/2-1)`
`[" By using " int e^(x)[ f(x)+f'(x)]dx=e^(x)f(x)] `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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  18. The value of int(-pi)^(pi) sin^(3) x cos^(2) x dx is equal to

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  19. The value of int(-1)^(1) log ((x-1)/(x+1))dx is

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