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The value of lim(x->oo)(int0^x(tan^(-1)x...

The value of `lim_(x->oo)(int_0^x(tan^(-1)x)^2)/(sqrt(x^2+1))dx`

A

`pi//4`

B

`pi^(2) //2`

C

`pi^(2) //4`

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
C
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MCGROW HILL PUBLICATION-DEFINITE INTEGRALS-EXERCISE (LEVEL 1) Single Correct Answer Type Questions
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  2. overset(1)underset(0)int |sin 2pi x|dx id equal to

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

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

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

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

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

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

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

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

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

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

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

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  14. The greatest value of the function F(x)= int(4)^(x) (t^(2) -8t+16) dt ...

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  15. If for a continuous function f, int(-a)^(a) f(x)dx = K int(0)^(a) (f(x...

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  16. If I(n)=int(1)^(e)(log x)^(n)dx then I(8)+8I(7)=

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  17. Let f(1) (x)= int(0)^(x) f(t) dt, f(2) (x) = int(0)^(x) f(1) (t) dt an...

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  18. If variables x and y are related by the equation x=underset(0)overse...

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  19. If y= f(x) be an invertible function with inverse g and h(x) = x f(x)...

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  20. The value of int(0)^([x]) (2^t)/( 2^([t]) ) dt

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