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int(0)^(pi)(1)/(1+sin x)dx is equal to...

`int_(0)^(pi)(1)/(1+sin x)dx` is equal to

A

1

B

2

C

`-1`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
B
Let ` l = int_(0)^(pi) 1/(1+sin x) dx`
` = int _(0)^(pi) 1/(1+(2tan.x/2)/(1+tan^(2).x/2))dx = int _(0)^(pi) (sec^(2)x/2)/((1+tan.x/2)^(2))dx `
Put ` tan x/2 = t`
` rArr 1/2 sec^(2). x/2 dx = dt` ,
Also ,at x = 0 , t=0 at `x = pi , t=alpha`
` :. l = int _(0)^(oo) (2dt)/(1+t)^(2) = [ 2/(1+t)]_(0)^(oo) = 2 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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  5. The value of int0^oox/((1+x)(x^2+1))dx is

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  6. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

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

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