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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-DEFINITE INTEGRATION -Exercise (Single)
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  2. The value of int(0)^(pi)(|x|sin^(2)x)/(1+2+cosx|sinx)dx is equal to

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  3. The value f the integral int(-pi)^pisinm xsinn xdx , for m!=n(m , n in...

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  4. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

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

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  6. int(-pi/2)^(pi/2)(e^(|sinx|)cosx)/((1+e^(tanx))dxi se q u a lto e+1 ...

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  7. The value of int(-pi)^(pi)(2x(1+sinx))/(1+cos^(2)x)dx is

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  8. [ The value of int(-pi)^( pi)sum(r=0)^(999)cos rx(1+sum(r=1)^(999)sin ...

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  9. Let T >0 be a fixed real number. Suppose f is continuous function such...

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  10. int1^4(x-0. 4)dxe q u a l s(w h e r e{x}i safr a c t ion a lp a r tof(...

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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. int0^x[sint]dt ,w h e r ex in (2npi,(2n+1)pi),n in N ,a n d[dot] den...

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  13. int(0)^(x)(2^(t))/(2^([t]))dt, where [.] denotes the greatest integer ...

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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. Ifg(x)=int0^x(|sint|+|cost|)dt ,t h e ng(x+(pin)/2) is equal to, wher...

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  16. Ifx=intc^(sint)sin^(-1)z dz ,y=intk^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)...

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  17. Let f(x)=int(2)^(x)(dt)/(sqrt(1+t^(4))) and g be the inverse of f then...

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  18. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

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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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  20. A function f is continuous for all x (and not everywhere zero) such th...

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