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Prove that : int(0)^(pi//2) (sqrt(cos x)...

Prove that : `int_(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx=(pi)/(4)`

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NAGEEN PRAKASHAN-INTEGRATION-Exercise 7p
  1. Prove that : int(0)^(pi//2) (sqrt(tanx))/(sqrt(tanx +sqrt(cotx)))dx=(p...

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  2. Prove that : int(0)^(pi//2) (sqrt(cos x))/(sqrt(sin x+ sqrt(cos x)))dx...

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  3. Prove that : int(0)^(pi//2) (sin^(3)x)/(sin^(3) x+ cos^(3)x)dx =(pi)/(...

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  4. Prove that : int(0)^(pi//2) (cos^(5))/(sin^(5) x+cos^(5) x)dx= (pi)/(4...

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  5. Prove that: int(0)^(pi//2) (1)/(1+tan^(3)x)=(pi)/(4)

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  6. Prove that : int(0)^(pi//2) (sin x-cos x)/(1+sin x cos x)dx=0 (ii) P...

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  7. Prove that : int(0)^(pi) x cos^(2) x dx =(pi^(2))/(4)

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  8. Prove that : int(0)^(a) (sqrt(x))/(sqrt(x)+sqrt(a)-x)dx=(a)/(2)

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  9. Prove that : int(0)^(pi) sin^(2) x . cos x dx =0

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  10. Prove that : int(0)^(pi//2) (sin x -cos x) log (sin^(3) x + cos^(3)x) ...

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  11. Prove that : int(2)^(7) (sqrt(x))/(sqrt(9-x)+sqrt(x))dx=(5)/(2)

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  12. Prove that : int(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

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  13. Prove that : int(0)^(pi//2)(x)/(sin x +cos x)dx= (pi)/(4sqrt(2)) log |...

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  14. Prove that int0^(pi/2) \ sin^2 x / (1+sin x cos x) \ dx = pi/(3 sqrt(3...

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  15. Evaluate : int(0)^(1) (1-x)^(3//2) dx

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  16. Evaluate : int(0)^(1)log ((1)/(x) -1) dx

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  17. Evaluate : int0^1x(1-x)^5dx

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  18. Evaluate : int(0)^(4) x(4-x)^(3//2)dx

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  19. Prove that :(i) int(-pi)^(pi) x^(10) sin^(7) x dx =0 (ii) int(-pi)^(...

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  20. int0^pi x tanx / (sec x + cos x) dx = pi^2 / 4

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