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If int(0)^(pi//2) cos^(n)x sin^(n) x dx=...

If `int_(0)^(pi//2) cos^(n)x sin^(n) x dx=lambda int_(0)^(pi//2) sin^(n)x" dx"`, then `lambda=`

A

`(1)/(2^(n-1))`

B

`(1)/(2^(n+1))`

C

`(1)/(2^(n))`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. If I=int(0)^(1) (dx)/(1+x^(4)), then

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  2. The value of int(-1)^(1) x|x|dx, is

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  3. If int(0)^(pi//2) cos^(n)x sin^(n) x dx=lambda int(0)^(pi//2) sin^(n)x...

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  4. The value of int(1//e )^(e )(|log x|)/(x^(2))dx, is

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  5. Assuming that f is everywhere continuous, (1)/(c )int(ac)^(bc)f((x)/(c...

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  6. (d)/(dx)(int(f(x))^(g(x)) phi(t)dt) is equal to

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  7. If f(x)=ae^(2x)+be^(x)+c x satisfies the conditions f(0)=-1, f'(log 2)...

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  8. The value of int(0)^(2) |cos((pix)/(2))| is

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  9. If int(0)^(1) cot^(-1)(1-x-x^(2))dx=k int(0)^(1) tan^(-1)x dx, then k=

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  10. If 0 lt a lt 1, then int(-1)^(1) (1)/(sqrt(1-2ax+a^(2)))dx is equal to

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  11. The value of int(0)^(pi//2) (x+sin x)/(1+cos x)dx, is

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  12. f(x)=|{:(sec x,cos x,,sec^(2) x+cosecx cot x),(cos^(2) x,cos^(2) x,,co...

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  13. If a is a fixed real number such that f(a-x)+f(a+x)=0, then int(0)^(2a...

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  14. The value of int(0)^(1) log((4+3 sin x)/(4+3 cos x))dx, is

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

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  16. The value of int(0)^(2pi) |cos x -sin x|dxis

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  17. If I(1)=int(0)^(1) 2^(x^(2)) dx, I(2)=int(0)^(1) 2^(x^(3)) dx, I(3)=in...

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  18. Consider the integrals I(1)=int(0)^(1)e^(-x)cos^(2)xdx,I(2)=int(0)^(...

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  19. If f(x)=f(a+b-x) for all x in[a,b] and int(a)^(b) xf(x) dx=k int(a)^(b...

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  20. To find the numberical value of int(-2)^(2) (px^(3)+qx+8)dx it is nece...

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