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The value of int(0)^(1) tan^(-1)((2x-1)/...

The value of `int_(0)^(1) tan^(-1)((2x-1)/(1+x-x^(2)))dx` is

A

1

B

0

C

-1

D

2

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The correct Answer is:
B
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STATEMENT 1: The value of int_(0)^(1)tan^(-1)((2x-1)/(1+x-x^(2)))dx=0 STATEMENT 2:int_(a)^(b)f(x)dx=int_(0)^(b)f(a+b-x)dx

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int_(0)^(1)Tan^(-1)((2x)/(1-x^(2)))dx=

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int tan^(-1)((1)/(1-x+x^(2)))dx

The value of int_0^1tan^(-1)((2x-1)/(1+x-x^2))dx ,\ is 1 b. -1 c. 0 d. pi//4

The value of int_(0)^(1)(tan^(-1)x)/(cot^(-1)(1-x+x^(2))dx is____.

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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. If a is a fixed real number such that f(a-x)+f(a+x)=0, then int(0)^(2a...

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  2. The value of int(0)^(1) log((4+3 sin x)/(4+3 cos x))dx, is

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  3. The value of int(0)^(1) tan^(-1)((2x-1)/(1+x-x^(2)))dx is

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  4. The value of int(0)^(2pi) |cos x -sin x|dxis

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  5. If I(1)=int(0)^(1) 2^(x^(2)) dx, I(2)=int(0)^(1) 2^(x^(3)) dx, I(3)=in...

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  6. Consider the integrals I(1)=int(0)^(1)e^(-x)cos^(2)xdx,I(2)=int(0)^(...

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  7. If f(x)=f(a+b-x) for all x in[a,b] and int(a)^(b) xf(x) dx=k int(a)^(b...

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  8. To find the numberical value of int(-2)^(2) (px^(3)+qx+8)dx it is nece...

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  9. Let f:R to R be continuous functions. Then the value of the integral i...

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  10. The value of int(-1//2)^(1//2) |xcos((pix)/(2))|dx is

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  11. The value of the integral int(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

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  12. The value of int(pi//2)^0 (1)/(9 cosx+12 sinx)dx is

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  13. If I=int(3)^(4) (1)/(3sqrt(logx))dxthen

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  14. If I=int(0)^(1//2) (1)/(sqrt(1-x^(2n)))dxthen which one of the follow...

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  15. If I=int(0)^(1//2) (sin^(2)n x)/(sin^(2)x)dxthen which one of the foll...

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  16. For any integer n, the integral int0^pie^(cosx)cos^3(2n+1)xdx has the ...

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  17. The value of the integral int(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal...

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  18. If int(0)^(oo) (log(1+x^(2)))/(1+x^(2))dx=kint(0)^(oo) (log(1+x))/(1+x...

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  19. If int(log2)^(x) (1)/(sqrt(e^(x)-1))dx=(pi)/(6)then x is equal to

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  20. The value of the integral overset(pi)underset(0)int log(1+cos x)dx is

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