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If f(x) is periodic function with period...

If f(x) is periodic function with period, T, then

A

`underset(a)overset(b)int f(x)dx=underset(a)overset(b+T)intf(x)dx`

B

`underset(a)overset(b)int f(x)dx=underset(a+T)overset(b)intf(x)dx`

C

`underset(a)overset(b)int f(x)dx=underset(a+T)overset(b+T)intf(x)dx`

D

`underset(a)overset(b)int f(x)dx=underset(a+T)overset(b+2T)intf(x)dx`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`underset(a+T)overset(b+T)int f(x)dx=underset(a)overset(b)intf(y+T)` dy, where `x=y+T`
`underset(a+T)overset(b+T)int f(x)dx=underset(a)overset(b)intf(x)dy[ :. "f is periodic with periodT" :. f(y+T)=f(y)]`
`underset(a+T)overset(b+T)int f(x)dx=underset(a)overset(b)intf(x)dx`
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Section I - Solved Mcqs
  1. If f(x) is an odd pefiodc function defined on the interval [T/2,T/2], ...

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  2. If int(pi//2)^(theta) sin x dx=sin 2 theta then the of theta satisfyin...

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  3. If f(x) is periodic function with period, T, then

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  4. The value of lim(n rarr infty) (1)/(n) {(n+1)(n+2)(n+3)…(n+n)}^(1//n)...

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  5. The points of extremum of phi (x)=int(1)^(x)e^(-t^(2//2)) (1-t^(2)) dt...

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  6. int(-2)^(2) min(x-[x],-x-[x])dx equals, where [x] represents greates i...

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  7. The integral int(0)^(a) (g(x))/(f(x)+f(a-x))dx vanishes, if

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  8. If (1)/(sqrt(a))int(1)^(a)((3)/(2)sqrt(x)+1-(1)/(sqrt(x)))dx lt4 then ...

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  9. Evaluate (int(0)^(n)[x]dx)/(int(0)^(n){x}dx) (where [x] and {x} are in...

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  10. If f(x)=min{|x-1|,|x|,|x+1|, then the value of int(-1)^(1) f(x) dx is ...

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  11. The value of int(0)^(100)[ tan ^(-1)x] d x is equal to (where [.] den...

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  12. The value of int(-1)^(10) sgn (x-[x])dx is equal to (where, [.] denote...

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  13. If n in N, then int(-n)^(n)(-1)^([x]) dx equals

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  14. The value of :.int(0)^([x]) (2^(x))/(2^([x]))dx is

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  15. If f(x) is a function satisfying f((1)/(x))+x^(2)f(x)=0 for all non ...

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  16. If f(x)={(e^cosx sinx ,, |x| leq 2),(2 ,, other wise):}. Then int-2^...

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  17. The value of the integral int (e ^(-1))^(e ^(2))|(ln x )/(x)|dx is:

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  18. about to only mathematics

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  19. Let f: (0, infty) rarr R and F (x) = int(0) ^(x) f(t) dt . If F(x^(2)...

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  20. The integral int(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (wher...

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