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IfIn=int0^1x^n(tan^(-1)x)dx ,t h e np ro...

`IfI_n=int_0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t` `(n+1)I_n+(n-1)I_(n-2)=-1/n+pi/2`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If In=int0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI(n+1)=2^(-n...

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  2. Given that f satisfies |f(u)-f(v)|lt=|u-v| for u and v in [a , b]dot T...

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  3. IfIn=int0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)In+(n-1)I(n-2...

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  4. IfI=int(-20pi)^(20pi)|sinx|[sinx]dx(w h e r e[dot] denotes the greate...

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

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  6. The value of the integral int0^1sqrt((1-x)/(1+x))dx i s (a)pi/2+1 (b...

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  7. IfI(m , n)=int0^(pi/2)sin^m xcos^n xdx , Then show that I(m , n)=(m-1...

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  8. Evaluate: int0^pi(xsin2xsin(pi/2cosx))/(2x-pi)dx

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  9. If IK=int1^e(lnx)^kdx(k in I^+)dx(k in I^+), then find the value of...

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  10. If int0^x {int0^u f(t) dt}du is equal to (a) int0^x (x-u) f(u)du ...

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  11. Prove that: In=int0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N.

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  12. Solve the following 2lt=|x-2|lt=5

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  13. The value of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

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  14. It is known that f(x) is an odd function in the interval [-p/2, p/2] ...

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  15. If int(-1)^4 f(x) dx =4 and int2^4[3-f(x)]dx=7 then the value of int(...

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  16. If int0^(pi/2)logsinthetad(theta)=k , then find the value of int0^(pi...

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  17. Evaluate: int0^(pi/2)sinxcosxdx

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  18. Let f(x) is continuous and positive for x in [a , b],g(x) is continuou...

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  19. Evaluate: int(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest i...

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  20. STATEMENT 1 : The value of int(-4)^(-5)sin(x^2-3)dx+int(-2)^(-1)sin(x^...

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