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underset(1)overset(sqrt(3))int (1)/(1+x^...

`underset(1)overset(sqrt(3))int (1)/(1+x^(2))dx=`

A

`(pi)/12`

B

`(pi)/6`

C

`(pi)/4`

D

`(pi)/3`

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The correct Answer is:
A
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TARGET PUBLICATION-DEFINITE INTEGRALS-EVALUATIO TEST
  1. underset(1)overset(sqrt(3))int (1)/(1+x^(2))dx=

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  2. int0^1log(1+x)/(1+x^2)dx

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  3. For every integer n, int(n)^(n+1)f(x)dx=n^(2), then the value of int(0...

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  4. If f(x)+f(3-x)=0,then int(0)^(3)1/(1+2^(f(x)))dx=

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  5. int(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=

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  6. Let I=int0^n[x]dx,n > 0, where [ ] is G.I.F.,

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  7. If In = int0^(pi/2) (sin^2 nx)/(sin^2 x) dx, then

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

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

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

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

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

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

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

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

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

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

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

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

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

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