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Evaluate : int0^(pi/2)(2logsinx-logsi...

Evaluate : `int_0^(pi/2)(2logsinx-logsin2x)\ dx`

A

`(pi)/(2)log 2`

B

`-(pi)/(2)log 2`

C

`pi log 2`

D

`-pi log 2`

Text Solution

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The correct Answer is:
B
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MARVEL PUBLICATION-INTEGRATION - DEFINITE INTEGRALS -MULTIPLE CHOICE QUESTIONS (PART - B : Mastering The BEST)
  1. The solution for x of the equation int(sqrt(2))^x(dt)/(tsqrt(t^2-1))=p...

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  2. integrate int0^(2pi) e^x . sin (pi/4 + x/2) dx

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  3. Evaluate : int0^(pi/2)(2logsinx-logsin2x)\ dx

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  4. If int0^(pi)xf(sinx)dx=Aint0^(pi/2)f(sinx)dx, then A is

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  5. The integral underset(0)overset(a)int (g(x))/(f(x)+f(a-x))dx vanishes...

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  6. If I(n)=underset(0)overset(pi//4)inttan^(n)x dx, then (1)/(I(2)+I(4)...

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  7. The value int(-2)^(2) (plog ((1+x)/(1-x)) + q log ((1-x)/(1+x))^(-2) +...

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  8. lim(n to oo)((sum(r=1)^(n)r^(2))(sum(r=1)^(n)r^(3)))/((sum(r=1)^(n)r^(...

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  9. If : int(0)^(pi)ln(sin x) dx = k, then : int(0)^(pi//4)ln (1+tan x)=

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  10. int(pi/3)^(pi/2) sqrt(1+cosx)/(1-cosx)^(5/2) dx

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  11. int(-pi//2)^(pi//2)(sin^(2)x.cos^(2)x(sin x+cos x))dx=

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  12. If : int(ln 2)^(x)(1)/(sqrt(e^(t)-1))dt=(pi)/(6), then : x =

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  13. int(0)^(pi//2)sin x.cos x. sqrt(a^(2).sin^(2)x+b^(2).cos^(2)x)dx=

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  14. If int0^oo (x^2 \ dx)/((x^2+a^2)(x^2+b^2)(x^2+c^2)) = pi/(2(a+b)(b+c)(...

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  15. int(0)^(2) (2x-2)/(2x-x^(2)) dx is equal to

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  16. int(1)^(e^(99))(sin(pi.ln x))/(x)dx=

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  17. Evaluate : lim(n-> oo) (1^4+2^4+3^4+...+n^4)/n^5 - lim(n->oo) (1^3+2^3...

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

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  19. The value of int(8 log(1+x))/(1+x^(2)) dx is

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  20. Find lim(ntooo)(1/(n+1)+1/(n+2)+...+1/(6n))

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