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Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^...

Let `f(x)=(e^(x)+1)/(e^(x)-1) and int_(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1) dx= alpha "Then" , int_(-1)^(1) t^(3) f(t) dt` is equal to

A

0

B

`alpha`

C

`2 alpha`

D

None of these

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Verified by Experts

The correct Answer is:
C
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TARGET PUBLICATION-DEFINITE INTEGRALS-EVALUATIO TEST
  1. If In = int0^(pi/2) (sin^2 nx)/(sin^2 x) dx, then

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  2. The value of the integral intalpha^beta 1/(sqrt((x-alpha)(beta-x)))dx

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  3. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

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  4. If m and n are positive integers and f(m,n)=int(0)^(1)x^(n-1)(logx)^(m...

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  5. The least value of the function phi(x)=int((7pi)/6)^(x)(4sint+3cost)dt...

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  6. Prove that int(a)^(b)f(x)dx=(b-a)int(0)^(1)f((b-a)x+a)dx

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  7. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

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  8. If f(x) is a function satisfying f(1/x)+x^(2)f(x)=0 for all non zero x...

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  9. lim(ntooo)1/n[1+sqrt(n/(n+1))+sqrt(n/(n+2))+sqrt(n/(n+3))+………..+sqrt(n...

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  10. lim(n->oo)sum(n=1)^n(sqrt(n))/(sqrt(r)(3sqrt(r)+4sqrt(n))^2)

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  11. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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  12. int(0)^(100pi)(|sin^(3)x|+|cos^(3)x|)dx=

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  13. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

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  14. overset(2pi) underset(0)int(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx,n gt 0...

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  15. The equation int(-pi/4)^(pi/4){a|sinx|+(bsinx)/(1+cos^2x)+c}dx=0 where...

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  16. int(0)^(sqrt("log"(pi)/2))cos(e^(x^(2)))2xe^(x^(2))dx=

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  17. If f(x)=int(0)^(x)sin^(6)tdt, then f(x+pi)=

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  18. If f(x) is a polynomial of degree 2, such that f(0)=3,f'(0)=-7,f''(0)=...

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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 f(x)=|(sin x+sin x 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,...

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