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The value f the integral int(-pi)^pisinm...

The value f the integral `int_(-pi)^pisinm xsinn xdx ,` for `m!=n(m , n in I),i s` 0 (b) `pi` (c) `pi/2` (d) `2pi`

A

`0`

B

`pi`

C

`pi//2`

D

`2pi`

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(-pi)^(pi) sin n x sin mx dx=int_(0)^(x) 2 sin mx sin nx dx`
`=int_(0)^(pi) [cos(m-n)xcos(m+n)x]dx`
`=|(sin(m-n)x)/(m-n)-(sin(m+n)x)/(m+n)|_(0)^(pi)=0`
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CENGAGE ENGLISH-DEFINITE INTEGRATION -SCQ_TYPE
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  7. Evaluate the following definite integral: int(-pi)^(pi)(2x(1+sinx))/(1...

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  11. The value of int0^x[cost]dt ,x in [(4n+1)pi/2,(4n+3)pi/2]a n dn in N ...

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  12. Evaluate int(o)^(2pi)[sin x]dx, where [.] denotes the greatest integer...

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  13. int0^x(2^t)/(2^([t]))dt ,w h e r e[dot] denotes the greatest integer f...

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  14. f is an odd function, It is also known that f(x) is continuous for all...

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  15. If g(x)=int0^x(|sint|+|cost|)dt ,t h e ng(x+(pin)/2) is equal to, whe...

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  16. If x=intc^(sint)sin^(-1)z dz ,y =intk^(sqrt(t))(sinz^2)/zdz, then (dy)...

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  18. If f(x) is differentiable and int0^(t^2) x f(x) dx=2/5t^5, then f(4/(2...

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  19. If f(x)=cosx-int0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to ...

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