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Evaluate: ("lim")(xvecoo)((int0xe^x^2dx)...

Evaluate: `("lim")_(xvecoo)((int0xe^x^2dx)^2)/(int0x e^(2x)^2dx)`

A

`1`

B

`2`

C

`3`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
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MCGROW HILL PUBLICATION-DEFINITE INTEGRALS-EXERCISE (LEVEL 1) Single Correct Answer Type Questions
  1. The value of int (-1)^(1) x|x| dx is

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  2. The difference between the greatest and least values of the function ...

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  3. Evaluate: ("lim")(xvecoo)((int0xe^x^2dx)^2)/(int0x e^(2x)^2dx)

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  4. The absolute value of underset(10)overset(19)int (cosx)/(1+x^(8))dx, ...

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  5. The value of the integral overset(3)underset(0)int (dx)/(sqrt(x+1)+sqr...

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  6. Let f(x) = {x}, the fractional part of x then int(-1)^(1) f(x) dx is e...

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  7. The value of int(-pi//2)^(pi//2) cos t sin (2t- pi//4) dt is

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

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  9. overset(1)underset(0)int |sin 2pi x|dx id equal to

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  10. The value of lim(x->oo)(int0^x(tan^(-1)x)^2)/(sqrt(x^2+1))dx

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  11. If A (t) = int(-1)^(t) e^(-|x|) dx, then lim( t to oo) A (t) is equal ...

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  12. If the value of int(-2)^(2) | x cos pi x| dx = k//pi then the value of...

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  13. The value of the integral underset(0)overset(pi)int (xdx)/(1+cos alpha...

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  14. The value of lim( n to oo) ((1)/(n) + (n)/((n+1)^2) + (n)/( (n+2)^2) +...

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  15. The value of lim(n to oo)((1)/(1^(3)+n^(3))+(2^(2))/(2^(3)+n^(3))+.......

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  16. For any n in N, the value of the intergral underset(0)overset(pi)int (...

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  17. If f(x)=Asin((pix)/2)+B, f'(1/2)=sqrt2 and int0^1 f(x)dx=(2A)/pi then ...

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  18. If (d)/(dx)f(x)=g(x) for a le x le b then, overset(b)underset(a)int f...

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  19. Let I(1) = int(a)^(b) (int(a)^(x) f(t) dt) dx and I(2) =int(a)^(b) (b-...

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  20. The least value of the function F(x) = int(x)^(2) log(1//3) t dt, x in...

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