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Suppose that `f: R to R ` is a continuous periodic function and T is the period of it . Let a `in R` . Then prove that for any positive integer n ` int_(0)^(a+nT) f(x)dx=n int_(a)^(a+T) f(x) dx`

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The correct Answer is:
`underset(a) overset(a+T)int f(x) dx`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DEFINITE INTEGRALS-Exercise -7(b)
  1. Evaluate the limit . lim(n to oo)l [(1+(1)/(n^(2)))(1+(2^(2))/(n^(2...

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  2. Evaluate the limit . lim(n to 00) ((n!)^(1/n))/(n)

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  3. Evaluate the integral int(0)^(pi//2) (dx)/(4+5cosx )

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  4. Evaluate the integral int(a)^(b) sqrt((x-a)(b-x))dx

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  5. Evaluate the integral int(0)^(1//2) (xsin^(-1)x)/(sqrt(1-x^(2))dx

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  6. Evaluate the integral I=int(0)^(pi//4) (sinx+cosx)/(9+16sin2x)dx

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  7. Evaluate the integral int(0)^(pi//2) (asinx+bcosx )/(sinx +cosx)dx

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  8. Evaluate the integral int(0)^(a) x(a-x)^(n)dx

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  9. Evaluate the integral int(0)^(2)xsqrt(2-x)dx

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  10. Evaluate the integral int(0)^(pi) x sin^(3)x dx

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  11. overset(pi)underset(0)int(x)/(1+sinx)dx.

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  12. Evaluate the integral underset(0)overset(pi)int (x sinx)/(1+cos^(2)x...

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  13. Evaluate the integral int(0)^(1) (log(1+x))/(1+x^(2))dx

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  14. Evaluate the integral int(0)^(pi) (xsinx)/(1+cos^(2)x) dx

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  15. Evaluate the integral int(0)^(pi//4) log(1+tanx)dx

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  16. Evaluate the integral int(0)^(3/2) |x sinpix| dx

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  17. Evaluate the integral int(0)^(1) sin^(-1) ((2x)/(1+x^(2)))dx

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  18. Evaluate the integral int(0)^(1) x tan^(-1)x dx

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  19. Evaluate the integral int(0)^(pi) (x sinx)/(1+cos^(2)x) dx

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  20. Suppose that f: R to R is a continuous periodic function and T is the...

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