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int(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1...

`int_(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dx`has the value

A

`(pi^(2))/(6)`

B

`(pi^(2))/(12)`

C

`(pi^(2))/(24)`

D

none of these

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Verified by Experts

The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Exercise
  1. Evaluate: int(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}...

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  2. For any natural number n, the value of the integral int(0)^(sqrt(n))...

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  3. For any n in R^(+), the value of the integral int(0)^(n[x]) (x-[x])d...

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  4. Let d/(dx)F(x)=((e^(sinx))/x),x > 0. If int1^4 3/x e^sin (x^3)dx=F(...

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  5. The equation int(-pi//4)^(pi//4) {a|sin x|+(b sin x)/(1+cos x)+c}dx=...

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  6. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in...

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  7. The value of int(alpha)^(beta) x|x|dx, where a lt 0 lt beta, is

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  8. int(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dxhas the value

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  9. If [.] denotes the greatest integer function and f(x)={:{(3(x)-(5|x|...

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  10. Find the value of int(-1)^(1)[x^(2)+{x}]dx, where [.] and {.} denote t...

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  11. The value of int(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int(-1)^(1) cos^(-...

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  12. Let Delta(y)=|{:(y+a,y+b,y+a-c),(y+b,y+c,y-1),(y+c,y+d,y-b+d):}| and,...

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  13. If I=int0^(1) (1)/(1+x^(pi//2))dx, then\

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  14. If int(0)^(x) f(t)dt=x^(2)+2x-int(0)^(x) tf(t)dt, x in (0,oo). Then, f...

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  15. If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int(-1)^1...

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  16. If I(n)=int(0)^(pi) e^(x)(sinx)^(n)dx, then (I(3))/(I(1)) is equal to

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  17. Given that lim(n to oo)sum(r=1)^(n)(log(n^(2)+r^(2))-2logn)/(n)=log2...

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  18. Let f be a differentiable function such that f'(x) = f(x) + int(0)^(2)...

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  19. Let f be a differentiable function such that f'(x) = f(x) + int(0)^(2)...

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  20. The value of the integral int(-10)^(0) (|(2|x|)/([x]-3x)|)/(((2|x|)/(3...

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