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int(0)^(pi//2) sin 2x .tan^(-1)(sin x)dx...

`int_(0)^(pi//2) sin 2x .tan^(-1)(sin x)dx=`

A

`pi/2 -1`

B

`pi/2 +1`

C

`pi/2`

D

`1 - pi/2`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. If int(0)^(oo)(x^(2)dx)/((x^(2)+a^(2))(x^(2)+b^(2))(x^(2)+c^(2)))=(pi)...

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  2. int(0)^(pi) (1)/(3+2 sin x+ cos x)dx=

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  3. int(0)^(pi//2) sin 2x .tan^(-1)(sin x)dx=

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  4. int(0)^(1)(xSin^(-1)x)/(sqrt(1-x^(2)))dx=

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  5. int(0)^(pi//2) e^(x)((1+sin x)/(1+cos x))dx=

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  6. int(2)^(e) ((1)/(ln x) - (1)/((ln x)^(2)))dx=

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  7. If A = int(0)^(1) (e^(t))/(1+ t)dt then int(0)^(1) e^(t) ln (1 + t) dt...

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  8. int(0)^(1) ((1-x^(2))dx)/(x^(4)+x^(2)+1)=

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  9. If k int(0)^(1) x f (3 x) dx = int(0)^(3) t f(t) dt then k=

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  10. If (d)/(dx) f(x) = g(x) then int(a)^(b) f(x) g(x) dx=

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  11. Let (d)/(dx) f(x) = (e^(sin x))/(x) , x gt 0. If int(1)^(4) 3/x e^(s...

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  12. Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1andg(x) be a f...

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  13. Let F(x)= f(x) + f(1/x), where f(x)= int(1)^(x) (ln t)/(1+t)dt, then F...

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  14. If f(x)=(1+ tan x) [1+ tan(pi/4 - x)] and g(x) is a function with doma...

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  15. y= int(x)^(x^(2)) sqrt(5-t^(2))dt then the value of (dy)/(dx) at x= sq...

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  16. If int(e)^(x) t f(t)dt= sin x - x cos x - (x^(2))/(2) for all x in R -...

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  17. If int(0)^(b-c) f(x+c) dx = k int(b)^(c) f (x) dx then k=

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  18. If f is every where continuous function then 1/c int(ac)^(bc) f(x/c) d...

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  19. If int(0)^(pi) f(tan x) dx= lambda then int(0)^(2pi) f(tan x) dx=

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  20. int(0)^(2) (2x-2)/(2x-x^(2))dx=

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