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The value of int0^pi(sin(n+1/2)x)/(sin(x...

The value of `int_0^pi(sin(n+1/2)x)/(sin(x/2)dx` is

A

`(pi)/(2)`

B

0

C

`pi`

D

`2pi`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. The value of int(0)^(pi//2) x^(10) sin x" dx", is then the value of m...

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  2. The value of int(0)^(pi//2) (1)/(1+tan^(3)x)dx is

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  3. The value of int0^pi(sin(n+1/2)x)/(sin(x/2)dx is

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  4. If (d)/(dx)f(x)=g(x) for a le x le b then, int(a)^(b) f(x) g(x) dx eq...

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  5. For any integer n,the integral int(0)^(3) e^(sin^(2)x)cos^(3)(2n+1)x" ...

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  6. The value of the integral int(0)^(3) sqrt(3+x^(3))dxlies in the inter...

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  7. The value of the integral int(0)^(1) (1)/((1+x^(2))^(3//2))dx is

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  8. If I=int(0)^(2pi) sin^(2) x" dx", then

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  9. If int(0)^(1) f(x)=M,int(0)^(1) g(x)dx=N, then which of the following ...

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  10. The value of int( 0)^(pi//4) (pix-4x^(2))log(1+tanx)dx is

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  11. The value of int(-pi//2)^(pi//2) sin{log(x+sqrt(x^(2)+1)}dx is

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  12. The value of int(0)^(2pi) cos^(99)x dx, is

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  13. If f(a+x)=f(x), then int(0)^(na) f(x)dx is equal to (n in N)

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  14. If f(t) is a continuous function defined on [a,b] such that f(t) is an...

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  15. If f(x) is an integrable function over every interval on the real line...

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  16. If I(1)=int(3pi)^(0) f(cos^(2)x)dx and I(2)=int(pi)^(0) f(cos^(2)x) th...

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  17. If f(x) is a quadratic polynomial in x such that 6int0^1 f(x)dx-{f(0...

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  18. The value of integral int(-2)^(4) x[x]dx is

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  19. If h(a)=h(b), the value of the integral inta^b [f(g(h(x))]^(-1)f'(g...

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  20. If F(x)=(1)/(x^(2))int(4)^(x) [4t^(2)-2F'(t)]dt then F'(4) equals

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