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If f(n)=(int0^n[x]dx)/(int0^n{x}dx)(wher...

If `f(n)=(int_0^n[x]dx)/(int_0^n{x}dx)`(where,[*] and {*} denotes greatest integer and tractional part of x and `n in N).` Then, the value of `f(4)` is...

A

`(1)/(n -1)`

B

`1/n`

C

n

D

`n-1`

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The correct Answer is:
D
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. Let f(x)=minimum {|x|,1-|x|,1/4} for xepsilonR then the value of int-1...

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  2. If [x] dentoes the greatest integer less than or equal to x, then the ...

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  3. If f(n)=(int0^n[x]dx)/(int0^n{x}dx)(where,[*] and {*} denotes greatest...

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  4. int (0) ^(2npi) (|sin x | - [|(sin x )/(2) | ]) dx is equal to (where ...

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  5. The value of int (0) ^([x]){x} dx is

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  6. If f(x) and g(x) are continuous functions satisfying f(x) = f(a-x) an...

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  7. If f(a+b - x) = f(x) , then int(a)^(b) x f(x) dx is equal to

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  8. If int(0)^(pi) x f (sin x) dx = A int (0)^(pi//2) f(sin x) dx , then A...

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  9. If f(x)=(e^(2))/(1+e^(x)),I(1)=overset(f(a))underset(f(-a))int xg{x(1-...

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  10. The value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x)dx where agt 0, is

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

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  12. int(0)^(pi//2)(1)/(1+tan^(3)x)dx=

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  13. int (-1) ^(1) (x ^(4))/( 1 + e ^(x ^(7)))dx is

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  14. int (-1) ^(1) (sin x + x ^(2))/( 3 - |x|) dx

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  15. The value of overset(pi//4)underset(-pi//4)int(e^(x)sec^(2)x)/(e^(2x)-...

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  16. int ( -pi) ^(pi) (2x ( 1+ sin x ))/(1+ cos ^(2) x )

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  17. int (0) ^(pi) (cos ^(2) x ) dx,

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  18. If int0^11 (11^x)/(11^([x])) dx=k/(log 11) then value of k is (where [...

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  19. Let Tgt0 be a fixed real number. Suppose f is a cintinuous function s...

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  20. Let f: RvecR be a differentiable function having f(2)=6,f^(prime)(2)=1...

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