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The primitive of (1)/((x-a)^(3//2)(b-x)^...

The primitive of `(1)/((x-a)^(3//2)(b-x)^(1//2))` is

A

`(1)/(b-a)[(b-x)/(x-a)]^(1//2)+C`

B

`(3)/(4(b-a))[(b-x)/(x-a)]^(1//2)+C`

C

`(1)/(b-a)[(x-a)/(b-a)]^(1//2)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
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MCGROW HILL PUBLICATION-INDEFINITE INTEGRATION-SOLVED EXAMPLE ( LEVEL 1 ( SINGLE CORRECT ANSWER TYPE QUESTION ))
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  2. int(dx)/(sinx+cosx) is equal to

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  3. The primitive of (1)/((x-a)^(3//2)(b-x)^(1//2)) is

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  4. If f(x) is the primitive of (sin 3sqrt(x)log(1+3x))/((tan^(-1)sqrt(x))...

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  5. If the primitive of f(x) = (1)/(3 sin x + sin^(3) x) is equal to f(x) ...

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  6. The value of int (cos x)/(sin x + cos x) dx is

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  7. If the primitive of (1)/(e^(x)-1)^(2) is f(x) - log |g (x)| + C then

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  8. If (dx)/(sin^(4)x+cos^(4)x)=(1)/(sqrt(2))tan^(-1)f(x)+C

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  9. The 1int(sin^(2)x)/(cos^(6)x)dx is a

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  10. If int tan^(7) x dx = f(x) + C then

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  11. If int(dx)/(sin x cos x)=log|f(x)|+C then

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  12. If polynomials P and Q satisfyint[(3x-1)cosx+(1-2x)sinx ]dx=P cosx+Qsi...

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  13. Let f(x) = inte^(x^(2))(x-2)(x-3)(x-4)dx then f increases on

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  14. int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1))dx is equal to

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  15. Let I =int(e^(x))/(e^(4x)+e^(2x)+1)dx , J = int(e^(-x))/(e^(-4x)+e^(-...

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  16. The value of sqrt(2)int(sinx)/(sin(x-(pi)/(4)))dx , is

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  17. If int[log(logx)+(1)/((logx)^(2))]dx =x[f(x) - g(x)] + C, then :

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  18. If f((3x-4)/(3x+4))=x+2, then int f(x)dx is equal to

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  19. intcos{2tan^(-1)sqrt((1-x)/(1+x))}dx is equal to

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  20. If u =-f''(theta) sintheta + f'(theta) costheta and v = f''(theta) cos...

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