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The value of the integral int(-pi//2)^(p...

The value of the integral `int_(-pi//2)^(pi//2) (x^(2)+ln'(pi+x)/(x-a)) cosx dx` is

A

0

B

`(pi^(2))/(2) - 4`

C

`(pi^(2))/(2) +4`

D

`(pi^(2))/(2)`

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The correct Answer is:
B
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. Let f : [-1,2]rarr[0,oo) be a continuous function such that f(x) = f(1...

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  2. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

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  3. The value of the integral int(-pi//2)^(pi//2) (x^(2)+ln'(pi+x)/(x-a)) ...

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  4. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

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  5. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

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  6. If f(x) = int(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , t...

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  7. The area enclosed by the curvesy= sinx+cosx and y = | cosx-sin x | ove...

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  8. Let f : [1/2, 1] rarr R (the set of the all real numbers) be a positiv...

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  9. For a in R (the set of all real numbers), a ne = - 1, lim(nrarroo)((...

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  10. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

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  11. Let f : (0,oo) rArr R be given f(x) = underset(1/x)overset(x)e^((1+(dt...

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  12. The value of int(0)^(1) 4x^(3){(d^(2))/(dx^(2))(1-x^(2))^(5)}dx is

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  13. The following integral int(pi/4)^(pi/2)(2cosecx)^(17) dx is equal to

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  14. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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  15. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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  17. Let f : R rarr R be a function defined by f(x) ={{:([x],xle2),(0,xgt...

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  18. If alpha = int(0)^(1)e^(9x+3tan^(-1)x)) ((12+9x^(2))/(1+x^(2)))dx wher...

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  19. Let f: RvecR be a continuous odd function, which vanishes exactly at o...

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  20. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^4x-3tan^2x for all x in (-pi/2,...

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