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Evaluate int ((sin^(-1) sqrt(x)-cos^(-1)...

Evaluate `int ((sin^(-1) sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)))dx`.

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Verified by Experts

The correct Answer is:
`(2)/(pi) [ sqrt(x-x^(2))-(1-2x) sin^(-1)sqrt(x)]-x +c`.
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OMEGA PUBLICATION-INTEGRALS-Important Questions from Miscellaneous Exercise
  1. Evaluate int(pi//2)^(pi) e^(x) ((1-sin x)/(1-cosx))dx.

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  2. Evaluate : int(0)^(pi) (x tan x)/(sec x +tan x) dx.

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  3. Evaluate int(0)^(pi//4) (sin x cos x)/(cos^(2)x +sin^(4)x)dx.

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  4. Evaluate the definite integral: int(pi/6)^(pi/3) (sinx+cosx)/(sqrtsin2...

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  5. Evaluate the following integral int((e^(5logx)-e^(4logx)) dx)/((e^(3...

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  6. Evaluate int (1)/(sqrt(sin^(3)x sin (x+alpha))dx.

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  7. Show that : int(0)^(pi//2) (sqrt(tan x) +sqrt(cot x))dx=sqrt(2)pi.

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  8. Evaluate : int(0)^(pi) (x dx)/(a^(2)cos^(2)x +b^(2)sin^(2)x).

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  9. Evaluate int ((sin^(-1) sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^...

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  10. Evaluate : int(0)^(1//sqrt(2)) (1)/(sqrt(1-x^(2)))dx

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  11. Evaluate int(pi//2)^(pi) e^(x) ((1-sin x)/(1-cosx))dx.

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  12. Evaluate : int(0)^(pi) (x tan x)/(sec x +tan x) dx.

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  13. Evaluate int(0)^(pi//4) (sin x cos x)/(cos^(2)x +sin^(4)x)dx.

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  14. Evaluate the definite integral: int(pi/6)^(pi/3) (sinx+cosx)/(sqrtsin2...

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  15. Evaluate int (e^(5log x)-e^(4log x))/(e^(3log x)-e^(2log x))dx.

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  16. Evaluate int (1)/(sqrt(sin^(3)x sin (x+alpha))dx.

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  17. Show that : int(0)^(pi//2) (sqrt(tan x) +sqrt(cot x))dx=sqrt(2)pi.

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  18. Evaluate : int(0)^(pi) (x dx)/(a^(2)cos^(2)x +b^(2)sin^(2)x).

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  19. Evaluate int ((sin^(-1) sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^...

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  20. Evaluate : int(0)^(1//sqrt(2)) (1)/(sqrt(1-x^(2)))dx

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