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The value of the integral int0^pi (x sin...

The value of the integral `int_0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n) x)dx` is :

A

`pi`

B

`2pi`

C

`pi^(2)`

D

`1/2 pi^(2)`

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  2. lim(n rarr oo) 1/n sum(r=1)^(2n) r/squeroot(n^(2)+r^(2)) equals

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  3. The value of the integral int0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n...

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  4. Let f(x) = x - [x], for every real number x, where [x] is integral par...

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  5. int(pi//4)^(3pi//4) (dx)/(1 + cos x) is equal to :

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  8. The value of (5050 int0^(1) (1-x^(50))^(100)dx)/(int0^(1) (1-x^(50))^(...

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  9. lim(x rarr pi/4)( int2^(sec^(2)x) f(t) dt)/(x^(2)-pi^(2)/16) equals

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  10. The values of lim(x rarr 0) (1)/(x^(3)) int(0)^(x) (t In (1 + t))/(t^(...

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  11. lim(n rarr oo) {(1^(m)+2^(m)+3^(m)+…….+n^(m))/(n^(m+1))} equals

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  12. If I(1) = int0^(1) 2^(x^(2)) dx, I(2) = int0^(1) 2^(x^(3)) dx, I(3) = ...

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  13. The value of the integral, int3^6 (sqrt(x))/(sqrt(9 - x) + sqrt(x))dx ...

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  14. The solution for x of the equation : int(sqrt2)^(x) (dt)/(tsqrt(t^2 - ...

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  15. Let I = int0^1 (sin x)/(sqrtx) dx and J = int0^1 (cos x)/(sqrtx) dx. T...

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  16. int0^(pi) [cot x] dx, when [cdot] denotes the greatest integer functio...

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  17. int(-2)^(2) |x| dx =

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  18. Ifint0^(a) (1)/(1+4x^(2)) dx = pi/8 then a =

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

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  20. The value of the integralint0^(3alpha) cosec(x-alpha) cosec(x-2alpha)d...

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