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If overset(a)underset(0)int(1)/(1+4x^(2)...

If `overset(a)underset(0)int(1)/(1+4x^(2))dx=(pi)/(8)`, then a equals

A

`(1)/(4)`

B

`-(1)/(2)`

C

`(3)/(2)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given , ` int _(0)^(p) (dx)/(1+4x^(2))= pi/8` ,
` LHS = int _(0)^(p) (dx)/(1+4x^(2)) = 1/4 int _(0)^(p) (dx)/(1/4+x^(2)) = 1/4 xx (1)/(1/2) [ tan^(-1)(x/(1/2))]_(0)^(p)`
` rArr 1/2 (tan^(-1) 2p ) = pi/8`
` rArr tan^(-1) 2p = pi/4 rArr 2p = 1`
` rArr p = 1/2`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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  9. If int(0)^(1) tan^(-1) x dx = p , then the value of int(0)^(1) tan^(-1...

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

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

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