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

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

A

log2

B

`(pi)/(4)+log2`

C

`(pi)/(2)+log2`

D

`(pi)/(2)-log2`

Text Solution

Verified by Experts

The correct Answer is:
D
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CHHAYA PUBLICATION-MCQ ZONE -Question Paper 5
  1. The value of int(0)^(3)(3x+1)/(x^(2)+9)dx is equal to -

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  2. The value of int e^(x)((2+sin2x)/(1+cos2x))dx is equal to -

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

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  4. The value of int(a^((x)/(2)))/(sqrt(a^(-x)-a^(x)))dx is equal to -

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  5. The value of int(a)^(b)(x)/(|x|)dx, a lt b lt 0, is equal to -

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  6. If g(x)=(1)/(2) [f(x)-f(-x)] defined over -3 le x le 3 and f(x)=2x...

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  7. If I(n)=int(0)^((pi)/(4)) tan^(n)x dx, then the value of (I(8)+I(6)) ...

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  8. The value of lim(n to oo)sum(r=1)^(n)(1)/(n)e^((r)/(n)) is -

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  9. int(0)^(1) sqrt((1-x)/(1+x))dx is equal to -

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  10. If int(sinx dx)/( sin(x-a))=Ax+B log|sin(x-a)|+c, then the value of (A...

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  11. The value of int(-2)^(3) |1-x^(2)|dx is equal to -

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  12. If int(0)^(t^(2)) x f(x) dx=(2)/(5) t^(5) , t gt 0, then the value of...

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  13. If P=int(0)^(3pi)f(cos^(2)x) dx and Q=int(0)^(pi) f(cos^(2)x)dx, the...

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  14. The order and degree of differential equation (1+3(dy)/(dx))^((4)/(3)...

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  15. The solution of the differential equation (dy)/(dx)+P(x)y=0 is -

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  16. The solution of the equation (dy)/(dx)+y=e^(-x), y(0)=0 is -

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  17. The differential equation of the family of curves y^(2)=4a(x+a) is -

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  18. The differential equation cot y dx=x dy has a solution of the form ...

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  19. The integrating factor of the differential equation 3(dy)/(dx)+(3y)/(...

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  20. The degree of the differential equation ((d^(3)y)/(dx^(3)))^((2)/(3))-...

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