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The value of sum(n=1)^1000 int(n-1)^n e^...

The value of `sum_(n=1)^1000 int_(n-1)^n e^(x-[x])dx`, where `[x]` is the greatest integer function, is (A) `(e^1000-1)/1000` (B) `(e-1)/1000` (C) `(e^1000-1)/(e-1)` (D) `1000(e-1)`

A

`(e-1)/(1000)`

B

`1000 (e-1)`

C

`(e^(1000)-1)/(e-1)`

D

`(e^(1000)-1)/(1000)`

Text Solution

Verified by Experts

The correct Answer is:
B
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ML KHANNA-DEFINITE INTEGRAL-Problem set (5) (Multiple Choice Questions)
  1. The value of the integral overset(1)underset(-1)int (x-[2x])dx,is

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  2. int(0)^(3//2) [x^(2)] dx=

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  3. Evaluate : int(0)^(2)[x^(2)]dx

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  4. int(0)^(3) [x^(3)-3x^(2) + 2x] dx=

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  5. The value of int(-pi//2)^(199pi//2) sqrt((1+cos 2x))dx is

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  6. The expression (underset(0)overset(n)int[x]dx)/(underset(0)overset(n)i...

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  7. int(0)^(n^(2)) [sqrtx] dx=

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

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  9. int(3)^(6) 2[x] dx is equal to

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  10. If [.] denotes the greatest integer function, then int(0)^(oo) [2e^(-x...

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  11. Evaluate int(1)^(e^(6))[(logx)/3]dx, where [.] denotes the greatest in...

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  12. The value of the integral underset(e^(-1))overset(e^(2))int |(log(e)x)...

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  13. int(1//e)^e |log x|dx=

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  14. If [x] denotes the greatest integer function then int(0.5)^(4.5) [x] d...

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  15. int(0)^(5) [x] dx= ….., where [x] denotes the greatest integer functio...

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  16. The value of the integral int(0)^(2) x[x] dx is where [x] is greatest ...

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  17. int(-1)^(3) {|x-1|+ [x]} dx with usual notations is

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  18. The value of sum(n=1)^1000 int(n-1)^n e^(x-[x])dx, where [x] is the gr...

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  19. int(0)^(2pi) e^(cos x) cosx (sin x) dx=

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  20. int(0)^(pi//3) [sqrt3 tan x] dx, where [.] denotes the greatest intege...

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