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if [x] denotes the greatest integer less than or equal to x then integral `int_0^2x^2[x] dx` equals

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: int0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest inte...

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  2. If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int0^1f(x)dx=(2A...

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  3. if [x] denotes the greatest integer less than or equal to x then integ...

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  4. The value of int0^(2pi)[2sinx]dx ,w h e r e[dot] represents the great...

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  5. f(x)=int1^x(tan^(-1)(t))/t dt \ AAx in R^+, then find the value of f...

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  6. Let f be a positive function. Let I1=int(1-k)^k xf([x(1-x)])dx , ...

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  7. Find the points of minima for f(x)=int0^x t(t-1)(t-2)dt

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  8. Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4), then find the value of ...

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  9. If g(x)=int0^xcos^4tdt , then g(x+pi) equals (a)g(x)+g(pi) (b) g(...

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  10. Evaluate lim(x to 4)int4^x((4t-f(t)))/((x-4))dt

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  11. Evaluate: int(pi/4)^((3pi)/4)dx/(1+cosx)

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  12. If In=int0^1(1-x^5)^n dx ,t h e n(55)/7(I(10))/(I(11))is equal to

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  13. Let f be a one-to-one continuous function such that f(2)=3 and f(5)=7....

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  14. The integral int(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (wher...

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  15. Evaluate: int0^(e-1)(e^((x^2+2x-1)/2))/(x+1)dx+int1^e xlogx e^(x^(2-2)...

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  16. Evaluate lim(xrarr0)(x-int0^(x) cost^2dt)/(x^3-6x)

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  17. The value of 2^(2010)(int0 ^1x^(1004)(1-x)^(1004)dx)/(int0^1x^(1004)(...

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  18. If int(0)^(1)(e^(t))/(1+t)dt=a then find the value of int(0)^(1)(e^(t)...

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  19. If f(x)=x+int0^1t(x+t)f(t)dt ,then the value of 23/2f(0) is equal...

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  20. Let f:(0,oo)to(0,oo) be a differentiable function satisfying, int0^x(1...

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