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Evaluate int(0)^(1//2)(xsin^(-1)x)/(sqr...

Evaluate `int_(0)^(1//2)(xsin^(-1)x)/(sqrt(1-x^(2)))dx`.

A

`1/2+(sqrt(3)pi)/12`

B

`1/2-(sqrt(3)pi)/12`

C

`1/2+(sqrt(3pi))/12`

D

None of these

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The correct Answer is:
B
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TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
  1. int(0)^(1) x tan^(-1) x " "dx =

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  2. int(0)^(1//sqrt(2))(sin^(-1)x)/((1-x^(2))^(3//2))dx=?

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  3. Evaluate int(0)^(1//2)(xsin^(-1)x)/(sqrt(1-x^(2)))dx.

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  4. The value of int(pi//4)^(3pi//4)(x)/(1+sinx) dx .. . . . .

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  5. If f(y)=e^y,g(y)=y,y>0, and F(t)=int0^t f(t-y)g(y) dy, then

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  6. int(0)^(2x)d^(x/2).sin(x/2+(pi)/4)dx=

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  7. I10=int0^(pi/2)x^(10)sinx dx then I10+90I8 is (A) 10(pi/2)^6 (B) 10(p...

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  8. If int0^1 x log(1+x/2) \ dx=a+b log\ 2/3, then a and b are

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  9. If I(m,n)=int0^1 t^m(1+t)^n.dt, then the expression for I(m,n) in term...

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  10. The value of ((5050)int0^1(1-x^50)^100 dx)/(int0^1 (1-x^50)^101 dx) i...

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  11. int(5)^(10) ""(1)/((x-1)(x-2))dx is equal to

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  12. The value of int(1)^(3)(dx)/(x(1+x^(2))) is

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  13. The value of int(2)^(3)(x+1)/(x^(2)(x-1))dx is

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  14. Evaluate int(0)^(pi//4)(sinx+cosx)/(9+16sin 2x)dx.

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  15. the value of integral int0^2 (log(x^2+2))/(x+2)^2dx is

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  16. int(0)^(1)(sin^(-1)(x/2))/xdx=

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  17. If I(1)=overset(e^(2))underset(e )int(dx)/(logx)"and "I(2)=overset(2)u...

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  18. Let a, b and c be non - zero real numbers such that int (0)^(3) (3ax...

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  19. If int(-1) ^(4) f(x) dx=4and int(2)^(4) (3-f(x))dx=7, then int(-1) ^...

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  20. Ifg(x)= int(0)^(x) cos 4t dt, "then " g (x+pi) equals

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