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Evaluate : int0^(pi/2) (sin^(3/2)x)/(sin...

Evaluate : `int_0^(pi/2) (sin^(3/2)x)/(sin^(3/2)x+cos^(3/2)x)dx`.

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The correct Answer is:
`(pi)/4`
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By using the properties of definite integrals, evaluate the integral: int_0^(pi/2) (sin^(3/2)x)/(sin^(3/2)x+cos^(3/2)x)dx

int_0^(pi/2) sin^(3/2x)/(sin^(3/2)x+cos^(3/2)x)dx is equal to :

int_0^(pi/2) sin^(3/2x)/(sin^(3/2)x+cos^(3/2)x)dx is equal to :

int_0^(pi/2) sin^(3/2x)/(sin^(3/2)x+cos^(3/2)x)dx is equal to :

By using the properties of definte, prove that int_(0)^(pi//2)(sin^(3//2)x)/(sin^(3//2)x+cos^(3//2)x)dx=(pi)/4

Evaluate : int_0^(pi/2) sin^3x/(sin^3x+cos^3x)dx .

BETTER CHOICE PUBLICATION-INTEGRALS-PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE
  1. Find the following integrals intx/((x-1)(x-2)(x-3))dx

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  2. Find the following integral: int dx/sqrt(5x^2-2x)

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  3. Evaluate : int0^(pi/2) (sin^(3/2)x)/(sin^(3/2)x+cos^(3/2)x)dx.

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  4. Find the following integrals int(0)^(pi//2)(sin^(4)x)/(sin^(4)x+cos^...

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  5. Find the following integrals int0to(pi/2)(cos^(5)x)/(sin^(5)x+cos^(5...

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  6. Find the following integrals int(cosx)/(cos(x-alpha))dx

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  7. Find the following integrals int(cosx)/(cos(x+alpha))dx

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  8. Find the following integrals int e^(x)(sinx+cosx)dx

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  9. Evaluate the following integrals: int e^(x)(tanx+logsecx)dx

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  10. int e^x (cot x + log sin x)dx is equal to :

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  11. Evaluate the following integrals: int 2/((1-x)(1+x^(2)))dx

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  12. Find the following integrals int 7/((x+2)(x^(2)+4))

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  13. Find the following integrals int(2)^(8)|x-5|dx

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  14. Find the following integral: int 1/(1+tanx) dx

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  15. Find the following integrals int 1/(1-tanx)dx

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  16. Evaluate the following integrals : int1/(1+cosx)dx

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  17. Find the following integrals int xlog x dx

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  18. Evaluate inte^(x)((1+sinx)/(1+cosx))dx

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  19. Using properties of definite integral prove that int0^2 xsqrt(2-x)dx= ...

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  20. Prove that : int(0)^(1)x(1-x)^(n)dx=1/((n+1)(n+2))

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