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If int0^1e^ (-x^2) dx=a , then find the ...

If `int_0^1e^ (-x^2) dx=a ,` then find the value of `int_0^1x^2e^ (-x^2) dx` in terms of `a`.

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: lim(x->oo)((int0^xe^(x^2)dx)^2)/(int0^x e^(2x^2)dx)

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  2. If f(x)=1+1/x int1^x f(t) dt, then the value of f(e^-1) is

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  3. If int0^1e^ (-x^2) dx=a , then find the value of int0^1x^2e^ (-x^2) dx...

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  4. Ifint0^(f(x))t^2dt=xcospix ,t h e nf^(prime)(9)i s -1/9 (b) -1/3 (c...

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  5. IfIn=int0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I5+20 I3dot

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  6. The value of int0^1lim(n->oo)sum(k =0)^n(x^(k+2)2^k)/(k!)dx is: (a) e...

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  7. If I(n)=int(0)^(pi/2) sin^(n)x dx, then show that I(n)=((n-1)/n)I(n-2)...

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  8. If A=int0^1 x^(50)(2-2x)^(50)dx ,B=int0^1 x^(50)(1-x)^(50)dx , which ...

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

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

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

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

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

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

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

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

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

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

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

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