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int(1)^(x) (logx^(2))/x dx is equal to...

`int_(1)^(x) (logx^(2))/x dx` is equal to

A

`(logx)^(2)`

B

`(1)/(2)(logx)^(2)`

C

`(logx^(2))/(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` l = int _(1)^(x) (2log x)/x dx`
Put log ` x= t rArr (dx)/x = dt `
` :. l = 2 int _(0)^(1ogx) t dt = 2 [(t^(2))/2]_(0)^(logx)=(log x)^(2)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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  8. int(0)^(pi//2)(1)/((1+tanx))dx=?

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  10. The value of int (0)^(pi//2) log ("cosec "x) dx is

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  11. Which of the following is true ?

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  12. int(0)^(5) 1/((x-1)(x-2))dx is equal to

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  13. int(pi/4)^(pi/2) e^x(logsinx+cotx)dx

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  14. The value of int(0)^(pi) x sin^(3) x dx is

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  15. The value of int0 ^(pi/2) (cos3x+1)/(cosx - 1) dx is equal to

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  16. The value of underset(0)overset(1)int tan^(-1) ((2x-1)/(1+x-x^(2)))dx ...

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  17. If f is a continous function, then

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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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  20. int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)

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  21. int (1)^(2)e^(x) (1/x - 1/(x^(2)))dx is qual to

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