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Let y=(x-[x])^([x]) where [x] is greates...

Let `y=(x-[x])^([x])` where `[x]` is greatest integar function, then `int_(0)^(3)y dx` equals

A

`(5)/(6)`

B

`(2)/(3)`

C

`1`

D

`(11)/(6)`

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AAKASH INSTITUTE ENGLISH-INTEGRALS-Objective Type Questions (Only one answer)
  1. int(0)^(3)(|x|+|x-1|+|x-2|)dx equals

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  2. If for a real number y ,[y] is the greatest integral function less, th...

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  3. Let y=(x-[x])^([x]) where [x] is greatest integar function, then int(0...

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  4. Evaluate (int(0)^(n)[x]dx)/(int(0)^(n){x}dx) (where [x] and {x} are in...

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  5. If f(x)={(e^cosx sinx ,, |x| leq 2),(2 ,, other wise):}. Then int-2^...

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  6. Find the value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x))dx, agt0.

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  7. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x i...

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  8. I(1)=int(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I(2)=int(0)^(2pi)cos^(...

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  9. Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" an...

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  10. int(-2)^0{(x+1)^3+2+(x+1)cos(x+1)dx is equal to (A) -4 (B) 0 (C) 4 ...

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  11. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

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  12. Value of the definite integral int(-1/2)^(1/2)(sin^(- 1)(3x-4x^3)-cos^...

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  13. Let f(x)=int(0)^(x)(sin^(100)t)/(sin^(100)t+cos^(100)t)dt, then f(2pi)...

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  14. int(0)^(pi)(x.sin^(2)x.cosx)dx is equal to

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  15. int0^1000 e^(x-[x])dx

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  16. The value of the definite integral int(19)^37((x)^2+3(sin2pix))dx wher...

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  17. If l(n)=int(0)^((pi)/(4)) tan^(n) xdx show that (1)/(l(2)+l(4)),(1)/(l...

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  18. The value of ("lim")(n rarr oo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r...

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  19. underset(kto0) lim1/kint0^k(1+sin2x)^(1/x)dx

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  20. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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