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If f(x) = f(a+x) and int(0)^(a) f(x) dx ...

If f(x) = `f(a+x) and int_(0)^(a) f(x) dx = k, "then" int _(0)^(na) f(x)` dx is equal to

A

nk

B

`(n-1)k`

C

`(n+1)k`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `f(x)=f(a+x) and int_(0)^(a)f(x)dx=k`
`int_(a)^(na)f(x)dx=nint_(0)^(a)f(9x)=nk" "[because "f(x) is periodic function"]`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. The value of the integral int (0)^(pi//2) log | tan x| dx is

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  2. int (-pi//2)^(pi//2) sin^(4) x cos^(6) x dx is equal to

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  3. If f(x) = f(a+x) and int(0)^(a) f(x) dx = k, "then" int (0)^(na) f(x) ...

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  4. The value of int(0)^(sqrt(2)) [ x^(2)] dx where [*] is the greatest i...

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  5. int0^pi(x dx)/(a^2cos^2x+b^2sin^2x)

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  6. l=int(-2)^(1)(tan^(-1)x+"cot"^(-1)(1)/(x))dx is equal to

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  7. int(0)^(pi) x sin^(4) x dx is equal to

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  8. If int (0)^(pi//2) sin^(6) dx = (5pi)/32 , then the value of int (...

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  9. int (0)^(pi//4) [ sqrt(tan x)+ sqrt(cot x)] dx is equal to

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  10. Evaluate the following limit: lim(nto oo)[(n!)/(n^(n))]^(1//n)

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  11. Let a, b and c be non - zero real numbers such that int (0)^(3) (3ax...

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  12. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

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  13. Ifint(sinx)^1t^2f(t)dt=1=1-s inx ,w h e r ex in (0,pi/2), then find t...

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  14. The value of int (2)^(4) { |x-2|+|x-3|} dx is

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  15. int (-1)^(2) |x|^(3) dx is equal to

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  16. int (0)^(3) (3x+1)/(x^(2)+9) dx =

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  17. int (0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) thet...

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  18. The value of the integral int (-a)^(a) (xe^(x^(2)))/(1+x^(2)) dx is

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  19. int (-pi//2)^(pi//2) (dx)/(1+cosx) is equal to

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  20. The value of int (0)^(12a) (f(x))/(f(x)+f(12a-x))dx is

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