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int(0)^(1) cot^(-1) (1-x+x^(2))dx=...

`int_(0)^(1) cot^(-1) (1-x+x^(2))dx=`

A

`pi - ln 2`

B

`pi/2 - ln 2`

C

`pi + ln 2`

D

`pi/2 + ln 2`

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. int(-1)^(3)(Tan^(-1)""(x)/((x^(2)+1))+Tan^(-1)""(x^(2)+1)/(x))dx=

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  2. int(0)^(sin^(2)x) sin^(-1) sqrt(t) dt + int(0)^(cos^(2)x) cos^(-1) sqr...

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  3. int(0)^(1) cot^(-1) (1-x+x^(2))dx=

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  4. If for every ineger n , int(n)^(n+1) f(x) dx=n^(2) then the value of i...

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  5. If f(x)={{:(x^(2) " for " 0 le x le 1),(sqrt(x) " for "1 le x le 2):}...

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  6. If int(-3)^(2) f(x)dx= 7/3 and int(-3)^(9) f(x)dx= - 5/6 then int(2)^(...

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  7. If int(-1)^(4)f(x)dx=4andint(2)^(4)[3-f(x)]dx=7" then "int(-1)^(2)f(x)...

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  8. The value of the integral int(0)^(oo)(xlogx)/((1+x^(2))^(2))dx is

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  9. int(0)^(pi//2) (sin^(100)x-cos^(100)x)dx=

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  10. For m, n in N and m != n then the value of int(0)^(pi) sin m x " " sin...

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  11. For n in N, the value of int(0)^(pi) sin^(n) x*cos^(2n-1)x dx is

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  12. For n in N, int(0)^(2pi) (x sin^(2n)x)/(sin^(2n) x + cos^(2n) x) dx=

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  13. int(0)(pi//2) ( x dx)/(Sin x + Cos x)=

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  14. int(0)^(pi)(xdx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)=

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  15. int(0)^(pi) x f (sin x) dx is equal to

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  16. If int(0)^(pi)xf(sinx)dx=Aint(0)^(pi//2)(sinx)dx, then A is

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  17. int(pi//4)^(3pi//4) (x)/(1+sin x) dx=

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  18. If f(x)=(e^(x))/(1+e^(x)),I(1)=int(f(-a))^(f(a))xg{x(1-x)}dxandI(2)=in...

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  19. If f(t)=int(-t)^(t)(e^(-|x|))/(2)dx" then "lim(ttooo)f(t)=

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  20. int(-2)^(3) |1-x^(2)|dx=

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