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The value of int(0)^(1000)e^(x-[x])dx, i...

The value of `int_(0)^(1000)e^(x-[x])dx`, is ([.] denotes the greatest integer function) :

A

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

B

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

C

1000(e-1)

D

`(e-1)/(1000)`

Text Solution

Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Exercise
  1. Evaluate lim(xto oo) ((int(0)^(x)e^(x^(2))dx)^(2))/(int(0)^(x)e^(2x^(2...

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  2. The value of int(1)^(4) e^(sqrt(x))dx, is

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  3. The value of int(0)^(1000)e^(x-[x])dx, is ([.] denotes the greatest in...

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  4. The value of the integral int(0)^(100) sin(x-[x])pidx, is

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  5. The difference between the greatest and least values of the function p...

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  6. The value of int0^1 (2^(2x+1)-5^(2x-1))/(10^(x))dx is

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  7. The value of int(0)^(pi//2) (cos3x+1)/(2 cos x-1) dx is

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  8. The value of int(0)^(16pi//3) |sinx|dx is

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  9. If int(0)^(npi) f(cos^(2)x)dx=k int(0)^(pi) f(cos^(2)x)dx, then the va...

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  10. The value of int(-pi)^(pi) sinx f(cosx)dx is

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  11. If a lt int(0)^(2pi) (1)/(10+3 cos x)dx lt b. Then the ordered pair (a...

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  12. The value of the integral int0^oo(xlogx)/((1+x^2)^2)dx ,is (a)0 (...

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  13. The value of the integral int(-pi//2)^(pi//2) sqrt(cosx-cos^(2)x)dx is

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  14. The value of the integral int(-pi/2)^(pi//2) sqrt((1+cos2x)/(2))dx is

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  15. Let I(1)=int(1)^(2)(x)/(sqrt(1+x^(2)))dx and I(2)=int(1)^(2)(1)/(x)dx....

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  16. Evaluate the following integral: int0^(pi//4)(s in x+cosx)/(3+s in2x)d...

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  17. The value of the integral int(0)^(pi//4) (sin theta+cos theta)/(9+16 s...

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  18. Let d/(dx)F(x)=((e^(sinx))/x),x > 0. If int1^4 3/x e^sin x^3dx=F(k)-F...

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  19. If I=int(-1)^(1)([x^(2)]+log((2+x)/(2-x)))dx where [x] denotes the gre...

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  20. The value of int(-pi//2)^(pi//2)(x^(2)+x cosx+tan^(5)x+1)dx is equal t...

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