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

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  5. If f(x)={(e^(cosx)sinx, |x|le2),(2, otherwise):} then int-2^3f(x)dx= (...

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

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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^3+3x^2+3x+3+(x+1)cos(x+1)dxi se q u a lto -4 (b) 0 (c...

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

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

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

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

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  17. 1/kint0^k(1+sin2x)^(1/x)dx

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

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  19. Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex >...

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  20. If f(x)=[{:(sqrt(1-x), , , 0 le x le 1),((7x-6)^(-1) , , ,1 le x le 2)...

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