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3a int(0)^(1) ((ax-1)/(a-1))^(2) dx is...

`3a int_(0)^(1) ((ax-1)/(a-1))^(2) dx` is equal to

A

`a-1+(a-1)^(-2)`

B

`a+a^(-2)`

C

`a-a^(2)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
` 3a int _(0)^(1) ((ax-1)/(a-1))^(2) dx = (3a)/((a-1)^(2)) [ ((ax-1)^(3))/3xx1/a]_(0)^(1)`
` = 1/((a-1)^(2)) [ (a-1)^(3) +1]`
` = (a-1) +(a-1)^(-2)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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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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  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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