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If f(x) = cos x - cos^(2)x + cos^(3)x + ...

If `f(x) = cos x - cos^(2)x + cos^(3)x + …. to oo int f(x) dx =`

A

1

B

`pi/2-1`

C

`pi/2 -1/2`

D

`pi/4 - 1/4`

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  4. int(pi/4)^(pi/2) (cot^(4)x + cot^(2)x) dx =

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  5. If In = int0^(pi//4) tan^n x dx, then lim(n to oo) n [In + I(n -2)] eq...

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  6. If I(n) = int0^(pi/4) tan^(n)x dx, then n(I(n-1)+I(n+1)) =

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  8. int(1/sqrt3)^(x) (dx)/(1+x^(2)) = pi/6, then the upper limit x =

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  10. If int0^(k) (cos x)/(1+sin^(2)x) dx= pi/4 then k=

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  11. If int0^pi x f (sin x)dx = A int0^(pi//2) f (sin x) dx, then A is :

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  12. int(log (1/2))^(log2) sin ((e^(x)-1)/(e^(x)+1)) dx =

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  13. int0^(2pi) theta sin^2 theta cos theta d theta is equal to :

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  14. The value of integral int(-pi//4)^(pi//4) sin^(-4) x dx is :

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  15. If I(10) = int0^(pi/2) x^(10) sin x dx then I(10) + 90I(8) =

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  16. Let A = int0^(1) e^(t)/(t+1) dt, then int0^(1) (t.e^(t^(2)))/(t^(2)+1)...

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  17. If int0^(pi/2) (d theta)/(9 sin^(2) theta + 4 cos^(2) theta) = k pi, t...

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  18. Let f(x) = (e^(x)+1)/(e^(x)-1) and int0^(1)( (e^(x)+1)/(e^(x)-1)) x dx...

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  19. If int(-1)^(4) f(x) dx = 4 and int(2)^(4) f(x) dx = 7 then int2^(-1) f...

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  20. int0^(1) (sin^(2)x+cos^(x))/(cos^(x)+sin^(x)) x^(5) dx =

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