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Prove that : int(0)^(pi//2) (sin^(3)x)/(...

Prove that : `int_(0)^(pi//2) (sin^(3)x)/(sin^(3) x+ cos^(3)x)dx =(pi)/(4)`

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NAGEEN PRAKASHAN ENGLISH-INTEGRATION-Exercise 7p
  1. Prove that : int(0)^(pi//2) (dx)/(1+cot x)=(pi)/(4)

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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)...

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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(0)^(pi) sin^(2m) x. cos^(2m+1) x dx=0

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

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  13. Prove that : int(pi//4)^(3pi//4) (1)/(1+cos x) dx = 2

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  14. Evaluate : int((pi)/(4))^((3pi)/(4))(x)/(1+sinx)dx

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

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

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  17. Prove that : int(0)^(a) (dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)

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

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

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

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