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If [int0^1(dt)/(t^2+2tcosalpha+1)]x^2-[i...

If `[int_0^1(dt)/(t^2+2tcosalpha+1)]x^2-[int_- 3^3(t^2sin2t)/(t^2+1)dt]x-2=0 (0 < alpha < pi)` then the value of x is

A

`+-2sqrt((sin alpha)/(alpha))`

B

`+-sqrt((sin alpha)/(alpha))`

C

`+-4sqrt((sin alpha)/(alpha))`

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of alpha in [0,2pi] which does not satify the equation int(p...

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  2. lim(x to 0)(int(0)^(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

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  3. If [int0^1(dt)/(t^2+2tcosalpha+1)]x^2-[int- 3^3(t^2sin2t)/(t^2+1)dt]x-...

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  4. The number of value of alpha in the interval [-pi,0] satisfying sin...

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  5. The value of int(0)^(pi//2) (sin^(3)x cos x)/(sin^(4)x+ cos^(4)x )dx i...

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  6. The value of int0^pi1/(5+3cosx)dx is a. pi//2 b. pi//4 c. 0 d. pi...

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  7. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin((n-1))/...

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  8. underset(nrarr0)" lim" underset(r=1)overset(n)sum((r^(3))/(r^(4)+n^(4)...

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  9. The value of lim(n to oo) {(1+(1)/(n))(1+(2)/(n))(1+(3)/(n))...(2)}^(1...

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  10. Evaluate: (lim)(nvecoo)n[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

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  11. If I(n)=int(0)^(pi//4) tan^(n)x dx, (ngt1 is an integer ), then (a) I(...

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  12. If Im=int1^x(logx)^mdx satisfies the relation (Im)=k-l I(m-1) then

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  13. If I(m)=int(0)^(oo) e^(-x)x^(n-1)dx, "then" int(0)^(oo) e^(-lambdax) x...

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  14. If I(mn)=int(0)^(1)x^(m-1)(1-x)^(n-1)dx,(m, n epsilon I, m,n ge 0 ), t...

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  15. Find the points of maxima /minima of int(0)^(x^(2))(t^(2)-5t+4)/(2+e^(...

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  16. Evaluate the following definite integral: int(-pi)^(pi)(2x(1+sinx))/(1...

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

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

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

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

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