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If f(x) is an odd function defined on [-...

If f(x) is an odd function defined on `[-T//2,T//2]` and has period T, then `phi(x)=int_(a)^(x) f(t)dt` is

A

a periodic function with period `T//2`

B

a periodic function with period T

C

not a periodic function

D

a periodic function with period`T//4`

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Verified by Experts

The correct Answer is:
B
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. If h(a)=h(b), the value of the integral inta^b [f(g(h(x))]^(-1)f'(g...

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  2. If F(x)=(1)/(x^(2))int(4)^(x) [4t^(2)-2F'(t)]dt then F'(4) equals

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  3. If f(x) is an odd function defined on [-T//2,T//2] and has period T, t...

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  4. If for every integer n, int(n)^(n+1) f(x)dx=n^(2), then the value of ...

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  5. int(-pi+4)^(pi//4) (tan^(2)x)/(1+a^(x))dx is equal to

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  6. The value of int(0)^(pi//2) cosec(x-pi//3)cosec(x-pi//6)dx is

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  7. The value of int(-1)^(1) x|x|dx, is

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  8. int0^3 |x^(3)+x^(2)+3x|dx is equal to

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  9. The value of the integral int(0)^(3) (dx)/(sqrt(x+1)+sqrt(5x+1)) is

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  10. int(1)^(-1) (x^(3)+|x|+1)/(x^(2)+2|x|+1)dxis equal to

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  11. int(-pi/2)^(pi//2) log(e ){((ax^(2)+bx+c)/(ax^(2)-bx+c))(a+b)|sinx|}dx...

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  12. For any natural number n, the value of the integral int(0)^(sqrt(n))...

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  13. For any n in R^(+), the value of the integral int(0)^(n[x]) (x-[x])d...

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  14. If phi'(x)=(log(e )|sin x|)/(x),x ne pi,n in Z and int(1)^(3) (3log(...

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  15. The equation int(-pi//4)^(pi//4) {a|sin x|+(b sin x)/(1+cos x)+c}dx=...

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  16. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x i...

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  17. The value of int(alpha)^(beta) x|x|dx, where a lt 0 lt beta, is

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  18. int(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dxhas the value

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  19. If [.] denotes the greatest integer function and f(x)={:{(3[x]-(5|x|...

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  20. Find the value of int(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denot...

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