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Evaluate int (0)^(pi)(x)/(1+ cos^(2)x)dx...

Evaluate `int _(0)^(pi)(x)/(1+ cos^(2)x)dx`.

A

`(pi ^(2))/( sqrt2)`

B

`(pi ^(2))/( 2 sqrt2)`

C

`2 sqrt2 pi`

D

`(pi)/( 2 sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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DISHA PUBLICATION-INTEGRALS -EXERCISE-1 CONCEPT BUILDER
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  2. The value of int(1)^(e^(37))(pi sin(pi log x))/(x)dx is ………….

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  3. Evaluate int (0)^(pi)(x)/(1+ cos^(2)x)dx.

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  4. The value of int(pi//4)^(3pi//4)(phi)/(1+sinphi)d phi is

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  5. The value of int(0) ^(1) (dx )/( e ^(x) + e) is equal to

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  6. The value of int(-1)^(3)(|x|+|x-1|) dx is equal to

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  7. The value of int(-pi) ^(pi) (sin ^(2) x)/( 1 + 7 ^(x)) dx= is equal to

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  8. int ( log 1//2 ) ^( log 2) sin { (e ^(x) -1)/( e ^(x ) +1 )}dx equals

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  9. Let f (x) = x^(2) -2. If int (3) ^(6) f (x)dx =3f (c ) for some c in (...

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  10. int0^pix(sin^4xcos^4x)dx

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  11. If I(n) = int (0)^(pi//4) tan^(n) theta " " d theta, "then "I(8)+I(6)=

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  12. In=int0^(pi//4) tan^n x\ dx, then lim(ntooo) n\ [In + I(n+2)] is equal...

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  13. What is int tan^(2) x sec^(4) x dx equal to ?

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  14. int(0)^(pi//2) sin^(2) x cos ^(3) x dx

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  15. If int0^ooe^(-ax)dx=1/a, then int0^oo(x^n)e^(-ax)dx is

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  16. If I(m,n)= overset(1)underset(0)int x^(m) (ln x)^(n)dx then I(m,n) i...

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  17. What is the limiting value of the expression ({(n +1) (n+2).....(2n)...

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  18. (sum(n=1)^10int(-2n-1)^(-2n)sin^(27)(x)dx+sum(n=1)^10int(2n)^(2n+1)sin...

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  19. The limit, when the tends to infinity, of the series (sqrtn)/( sqrt ...

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  20. The series 1 + 1/2 + 1/3 +…..+ 1/n can be expressed by the definite in...

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