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If int0^(k) (cos x)/(1+sin^(2)x) dx= pi/...

If `int_0^(k) (cos x)/(1+sin^(2)x) dx= pi/4` then k=

A

1

B

`pi/4`

C

`pi/2`

D

`pi/3`

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  3. If int0^(k) (cos x)/(1+sin^(2)x) dx= pi/4 then k=

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  4. If int0^pi x f (sin x)dx = A int0^(pi//2) f (sin x) dx, then A is :

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  5. int(log (1/2))^(log2) sin ((e^(x)-1)/(e^(x)+1)) dx =

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  6. int0^(2pi) theta sin^2 theta cos theta d theta is equal to :

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  7. The value of integral int(-pi//4)^(pi//4) sin^(-4) x dx is :

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  8. If I(10) = int0^(pi/2) x^(10) sin x dx then I(10) + 90I(8) =

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  9. Let A = int0^(1) e^(t)/(t+1) dt, then int0^(1) (t.e^(t^(2)))/(t^(2)+1)...

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  10. If int0^(pi/2) (d theta)/(9 sin^(2) theta + 4 cos^(2) theta) = k pi, t...

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  11. Let f(x) = (e^(x)+1)/(e^(x)-1) and int0^(1)( (e^(x)+1)/(e^(x)-1)) x dx...

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  12. If int(-1)^(4) f(x) dx = 4 and int(2)^(4) f(x) dx = 7 then int2^(-1) f...

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  13. int0^(1) (sin^(2)x+cos^(x))/(cos^(x)+sin^(x)) x^(5) dx =

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  14. If beta +2 int0^(1) x^(2)e^(-x^(2)) dx = int0^(1) e^(-x^(2), then beta...

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  15. int0^(4/pi) (3x^(2) sin (1/x) - x cos (1/x)dx =

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  16. int0^(sqrtlog (pi/2)) cos(e^(x^(2))).2xe^(x^(2)) dx =

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  17. int0^(pi/2) (cosx-sinx)/(1+sinx cosx) dx =

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  18. int(-1/2)^(1/2) [sin^(-1)(3x-4x^(3)) - cos^(-1) (4x^(3)-3x)] dx =

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  19. int(-2)^(1) cot^(-1) (1/x) dx =

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  20. I = int(-2)^(1) (tan^(-1)x+ cot^(-1)(1/x) dx

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