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If f(X) is continuous and ninNthen the v...

If f(X) is continuous and `ninN`then the value of `int_-2^2{f(x)-f(-x)}x^(2n)dx`dx is

A

`nf(2)`

B

`2n`

C

`0`

D

none of these

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The correct Answer is:
C
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A DAS GUPTA-Properties and Application of definite Integrals-EXERCISE
  1. Evaluate: int0^(pi/2) (sin2x)/(sin^4x+cos^4x)dx

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  2. Let a, b, c be non-zero real numbers such that ; int0^1 (1 + cos^8 x)(...

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  3. If f(X) is continuous and ninNthen the value of int-2^2{f(x)-f(-x)}x^...

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  4. An extremum value of y=int0^x(t-1)(t-2)dt is : 5/6 (b) 2/3 (c) 1 ...

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  5. An AC voltage is given by E=E(0) sin(2pit)/(T). Then the mean value of...

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  6. If g(x)=int0^xcos^4tdt , then g(x+pi) equals g(x)+g(pi) (b) g(x)-g(pi...

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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. State whether the statements are true or false.If y=int0^xf(t)dt .Then...

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  9. State whether the statements are true or false.int0^(pi/2)dx/(sqrt(sin...

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  10. If int0^a{f(x)+f(-x)}dx=int-a^aphi(x)dxthen phi(x)=.

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  11. Evaluate: int0^pi (cos x)/(1+sinx)^2 dx

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  12. The value int(-pi/4)^(pi/4)x^2sin^-1xdx=.

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  13. If int0^pi x f(sinx) dx=A int0^(pi/2) f(sinx)dx, then A is (A) pi/2 (B...

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  14. The value of int0^(pi/2)sin2x.log tanxdx is

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  15. If int0^1e^t/(t+1) dt=a, then int(b-1)^b e^(-t)/(t-b-1) dt=

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  16. Evaluateint(-pi/2)^(pi/2)(sin2x)/(1+cos^3x)dx

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  17. If f is a continuous function on the interval [a,b] and there exists ...

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  18. If l(n)=int(1)^(e)(log x)^(n) d x, "then" l(n)+nl(n-1) equal to

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  19. If f(x)=|x-21|+|x-1|then evaluate int-2^2f(x)dx.

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  20. If f(x)=f(4-x), g(x)+g(4-x)=3 and int(0)^(4)f(x)dx=2, then : int(0)^(4...

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