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Let f(x) = x - [x], for every real numbe...

Let `f(x) = x - [x]`, for every real number x, where [x] is integral part of x. Then `int_(-1)^(1) f(x) dx` is:

A

`1`

B

`2`

C

`0`

D

`1/2`

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The correct Answer is:
A
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MODERN PUBLICATION-DEFINITE INTEGRALS-MULTIPLE CHOICE QUESTIONS (LEVEL - II)
  1. Let f(x) = x - [x], for every real number x, where [x] is integral par...

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  2. If int0^x f(t) dt = x + intx^l tf (t) dt, then the value of f(1) is :

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  3. If f(x) = A sin ((pi x)/(2)) + B , f' (1/2) = sqrt(2) and int0^1 f(x) ...

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  4. int(-1)^1 ((x^7 - 3x^5 + 7x^3 - x)/(cos^2 x) + cos^(-1)x)dx equals :

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  5. sum(n = 1)^(1000) int(n - 1)^(n) e^(x-[x]) dx, whose [x] is the greate...

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  6. If f(x) = |(sin x + sin 2x + sin 3x, sin 2x , sin 3x),(3 + 4 sin x, 3,...

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  7. lim(n to oo) {(n!)/((kn)^n)}^(1/n), where k != 0 is a constant and n i...

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  8. If f(x) is a quadratic polynomial such that f(0) = 2, f(0) = -3 and f'...

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  9. lim(n to oo) ((n)/(1 + n^2) + n/(2^2 + n^2) + n/(3^2 + n^2) + ……. + n/...

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  10. int0^(pi) (x tanx dx)/(sec x+ cosx) =

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  11. Let f : R to R be a differentiable function and f(1) = 4, then the val...

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  12. For any integer n, the integral : int0^(pi) e^(cos^2) cos^(3) (2n + 1)...

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  13. If In = int0^(pi//4) tan^n theta d theta, then for any +ve integer n, ...

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  14. int0^1 |sin 2 pi x| dx is equal to :

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  15. If f(x) = f(a - x), then int0^(a) xf(x) dx is equal to :

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  16. Let f(x) = {:[(e^(cos x) sinx",", "for" |x| le 2),(2,"otherwise"):} th...

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

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  18. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

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  19. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

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  20. If (1 sin t)/(1 + t) dt = alpha, then that value of the integral : i...

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