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The value of the integral int(alpha)^(be...

The value of the integral `int_(alpha)^(beta) sqrt((x-alpha)(beta-x))dx`, is

A

`(pi)/(4)(beta-alpha)^(2)`

B

`(pi)/(2)(beta-alpha)^(2)`

C

`(pi)/(8)(beta-alpha)^(2)`

D

none of these

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Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. int(-pi)^(pi) (2x(1+ sinx))/(1+ cos^(2))dx is

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  2. The value of the inntegral int(alpha)^(beta) (1)/(sqrt((x-alpha)(beta-...

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  3. The value of the integral int(alpha)^(beta) sqrt((x-alpha)(beta-x))dx,...

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  4. If int(0)^(x^(2)) sqrt(1=t^(2)) dt, then f'(x)n equals

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  5. The value of integral int(1)^(e) (log x)^(3)dx , is

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  6. If int(x^(2))^(x^(4)) sin sqrt(t) dt, f'(x) equals

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  7. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  8. The value of lim(n->oo) [(1+1/n^2)(1+2^2/n^2)...(1+n^2/n^2)]^(1/n)

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  9. If int(0)^(1) e^(x^(2))(x-alpha)dx=0 then

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  10. If f(x) satisfies the requirements of Rolle's Theorem in [1,2] and f(x...

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  11. The value of the integral int(0)^(1) cot^(-1) (1-x+x^(2))dx, is

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  12. The integral int(-1)^(1) (|x+2|)/(x+2)dx is equal to

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  13. Let I= int(0)^(1) (x^(x))/( x+1) dx, then the vlaue of the intergral ...

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  14. The value of the integral int(0)^(pi) (xdx)/(1+cos alpha sinx), 0 lt a...

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  15. int(pi)^(10n) |sin x|dx is equla to

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  16. If int0^pi 1/(a+bcosx)dx=pi/sqrt(a^2-b^2), then int0^pi 1/(a+bcosx)^2d...

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  17. If int(1)^(oo) e^(-ax) dx=(1)/(a),"then" int(1)^(oo) x^(n)e^(-ax)dx...

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  18. The value of int(pi)^(2pi) [ 2 sin x] dx, where [] repreents the great...

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  19. If f(x)=Asin((pix)/2)+B, f'(1/2)=sqrt2 and int0^1 f(x)dx=(2A)/pi then ...

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  20. If I(m,n)= int(0)^(1) x^(m) (ln x)^(n)dx then I(m,n) is also equal to

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