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If 2f(x) - 3 f(1//x) = x," then " int(1)...

If `2f(x) - 3 f(1//x) = x," then " int_(1)^(2) f(x) dx` is equal to

A

`(3//5)log2`

B

`(-3//5)(1+log2)`

C

`(-3//5)log2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `2f(x)-3f((1)/(x))=x`
Put `x=(1)/(x)` Eq . (i) , we get
`2f((1)/(x))-3f(x)=(1)/(x)`
On solving Eqs . (i) and (ii) , we get
`f(x)=-(3+2x^(2))/(5x)`
Now , `int_(1)^(2)f(x)dx=-int_(1)^(2)(3+2x^(2))/(5x)dx`
`=-int_(1)^(2)((3)/(5x)+(2x)/(5))dx`
`=(1)/(5)[3logx+(2x^(2))/(2)]_(1)^(2)`
`=-(1)/(5)(3 log2+4-2log1-1)`
`=-(1)/(5)(3log2+4-0-1]`
`=-(3)/(5)(1+log2)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
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  13. The value of overset(pi)underset(-pi)int(1-x^(2)) sin x cos^(2) x" dx"...

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  14. int (0)^(1) (xdx)/([x + sqrt(1-x^(2))]sqrt(1-x^(2))) is equal to

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  16. The value of int (-1)^(1) x|x| dx is

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  18. The value of int (1)^(e^(2)) (dx)/(x(1+ log x)^(2) ) is

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  20. The value of the integral overset(1)underset(0)int x(1-x)^(n)dx, is

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