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l=int(-2)^(1)(tan^(-1)x+"cot"^(-1)(1)/(x...

`l=int_(-2)^(1)(tan^(-1)x+"cot"^(-1)(1)/(x))dx` is equal to

A

` (5pi)/2+ 4 tan ^(-1) 2 - In 5/2`

B

` (5pi)/2 - 4 tan^(-1) 2 + In 5/2`

C

` (5pi)/2 - 3 tan ^(-1) 2 - In 5/2`

D

` (5pi)/2 - 3 tan ^(-1) 2 + 5/2`

Text Solution

Verified by Experts

The correct Answer is:
B
`l=int_(-2)^(1)(tan^(-1)+cot^(-1).(1)/(x))dx`
`=int_(-2)^(0)(tan^(-1)x+pi+tan^(-1)x)dx+int_(0)^(1)(tan^(-1)x+tan^(-1)x)dx`
`=int_(-2)^(0)2tan^(-1)xdx+int_(-2)^(0)pidx+int_(0)^(1)2tan^(1)xdx`
`=2[x tan^(-1)x-(1)/(2)log(1+x^(2))]_(-2)^(0)+[pix]_(-2)^(0)+2[x tan^(-1)x-(1)/(2)log(1+x^(2))]_(0)^(1)`
`=(5pi)/(2)-4tan^(-1)2+log.(5)/(2)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. The value of int(0)^(sqrt(2)) [ x^(2)] dx where [*] is the greatest i...

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  2. int0^pi(x dx)/(a^2cos^2x+b^2sin^2x)

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  3. l=int(-2)^(1)(tan^(-1)x+"cot"^(-1)(1)/(x))dx is equal to

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  4. int(0)^(pi) x sin^(4) x dx is equal to

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  5. If int (0)^(pi//2) sin^(6) dx = (5pi)/32 , then the value of int (...

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  6. int (0)^(pi//4) [ sqrt(tan x)+ sqrt(cot x)] dx is equal to

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  7. Evaluate the following limit: lim(nto oo)[(n!)/(n^(n))]^(1//n)

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

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  9. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

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  10. Ifint(sinx)^1t^2f(t)dt=1=1-s inx ,w h e r ex in (0,pi/2), then find t...

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  11. The value of int (2)^(4) { |x-2|+|x-3|} dx is

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  12. int (-1)^(2) |x|^(3) dx is equal to

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  13. int (0)^(3) (3x+1)/(x^(2)+9) dx =

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  14. int (0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) thet...

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  15. The value of the integral int (-a)^(a) (xe^(x^(2)))/(1+x^(2)) dx is

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  16. int (-pi//2)^(pi//2) (dx)/(1+cosx) is equal to

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  17. The value of int (0)^(12a) (f(x))/(f(x)+f(12a-x))dx is

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  18. If kint(0)^(1)xf(3x)dx=int(0)^(3)tf(t)dt, then the value of k is

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  19. lim(nto oo)+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+...(1)/(sqrt(n^(2...

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  20. lim(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)

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