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Evaluate: lim(x->oo)((int0^xe^(x^2)dx)^...

Evaluate: `lim_(x->oo)((int_0^xe^(x^2)dx)^2)/(int_0^x e^(2x^2)dx)`

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  2. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

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  3. Evaluate: lim(x->oo)((int0^xe^(x^2)dx)^2)/(int0^x e^(2x^2)dx)

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

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

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

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

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

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

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

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

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

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

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