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Definite Integration

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  1. 1.The value of the integral _0^2x(x^2+x+1)(x+1)(x^4+x^2+1)dx is equal to:
  2. 2.Let f(x)=array|c|c| (1)/(3), & x /2 b(1- x)( -2x)^2, & x> /2 array.
  3. 3.Let A=[[|gathered 1 3 -1 2 1 0 1 -1 gathered]]| be a singular matrix.
  4. 4.The value of the integral _-1^1(x^3+|x|+1x^2+2|x|+1)dx is equal to:
  5. 5.The value of the integral _-( )/(4)^( )/(4)(32 ^4x1+e^ x)dx is :
  6. 6.Let (2^1-a+2^1+a),f(a),(3^a+3^-a) be in A.P.
  7. 7.The value of the integral _0^ _e(x)x^2+4dx is:
  8. 8.The value of the integral _( )/(6)^( )/(3)(4- ^2x ^4x)dx is :
  9. 9.If =1 and =1+i√2, where i=-1 are two roots of the equation x^3+ax^2+bx+c=0,a,b, R, then _1…
  10. 10.The integral _0^1 ^-1(1+x+x^2)dx is equal to :
  11. 11.Let f be a real polynomial of degree n such that f(x)=f^'(x)f^''(x), for all x R.
  12. 12.Let _-2^2(| x|+[x x])dx=2(3- 2)+ , where [ ] is the greatest integer function.
  13. 13.The value of _0^20 ( ^4x+ ^4x)dx is equal to:
  14. 14.Let [.] denote the greatest integer function.
  15. 15.Let [.] denote the greatest integer function.
  16. 16.The value of the integral _(5 )/(24)^( )/(24)(dx)/(1+√3 2x) is :
  17. 17.The value of _-( )/(2)^( )/(2)((1)/([x]+4))dx, where [ ] denotes the greatest integer func…
  18. 18.Let f:[1,) R be a differentiable function.
  19. 19.The value of _- /6^ /6( +4x^111- (|x|+ /6))dx is equal to:
  20. 20.The integral _-1^(3)/(2)(| ^2x ( x)|)dx is equal to:
  21. 21.Let f(x) be a positive function and I_1= _-(1)/(2)^12x, f(2x(1-2x)), dx and I_2= _-1^2f(x(…
  22. 22.The integral _ ^0(x+3) x1+3 ^2xdx is equal to
  23. 23.Let f(x)+2f((1)/(x))=x^2+5 and 2g(x)-3g((1)/(x))=x,x>0.
  24. 24.The value of _-1^1(1+|x|-x)e^x+(|x|-x)e^-xe^x+e^-xdx is equal to
  25. 25.The integral _ ^08xdx4 ^2x+ ^2x is equal to
  26. 26.Let the domain of the function f(x)= _2 _4 _6(3+4x-x^2) be (a,b).
  27. 27.Let f:[1,) [2,) be a differentiable function.
  28. 28.Let (a, b) be the point of intersection of the curve x^2=2 y and the straight line y-2 x-6…
  29. 29.4 _1^0(1√3+x^2+√1+x^2)dx-3 _e(√3) is equal to :
  30. 30.Let f(x)= _0^xt(t^2-9t+20)dt,1 x 5.
  31. 31.The integral 80 _0^( )/(4)(( + )/(9+16 2 ))d is equal to :
  32. 32.Let f:R R be a twice differentiable function such that f(2)=1.
  33. 33.If _( )/(2)^-( )/(2)96x^2 ^2x(1+e^x)dx= ( ^2+ ), , Z, then ( + )^2 equals
  34. 34.If I(m,n)= _1^0x^m-1(1-x)^n-1dx,m,n>0, then I(9,14)+I(10,13) is
  35. 35.If I= _( )/(2)^0 ^(3)/(2)x ^(3)/(2)x+ ^(3)/(2)xdx, then _2I^0x x x ^4x+ ^4xdx equals :
  36. 36.The value of _e^4^e^2(1)/(x)(e^(( _ex)^2+1)^-1e^(( _ex)^2+1)^-1+e^((6- _ex)^2+1)^-1)dx is
  37. 37.Let for f(x)=7 ^8x+7 ^6x-3 ^4x-3 ^2x,, I_1= _ /4^0f(x)dx and I_2= _ /4^0xf(x)dx.
  38. 38.x ( )/(2)lim( _( /2)^3^x^3( (2t^1/3)+ (t^1/3))dt(x-( )/(2))^2) is equal to
  39. 39.The value of the integral _-1^2 _e(x+x^2+1)dx is
  40. 40.Let _ ^ _e4dxe^x-1=( )/(6).
  41. 41.The value of k N for which the integral I_n= _1^0(1-x^k)^ndx,n N, satisfies 147I_20=148I_2…
  42. 42._0^ /4 ^2x ^2x( ^3x+ ^3x)^2dx
  43. 43.Let (m,n)= _0^1x^m-1(1-x)^n-1dx,m,n>0.
  44. 44.The value of _- ^ 2y(1+ y)1+ ^2ydy is :
  45. 45.Let f(x)= _x^0(t+ (1-e^t))dt,x R.
  46. 46.If the value of the integral _-1^1 x1+3^xdx is (2)/( ).Then, a value of is
  47. 47.f(x)= array|c|c| -2, & -2 x 0 x-2, & 0<x 2 arrayh(x)=f(|x|)+|f(x)| _-2^2h(x)dx
  48. 48.If _0^( )/(3) ^4xdx=a +b√3, where a and b are rational numbers, then 9a+8b is equal to :
  49. 49.The value of _0^1(2x^3-3x^2-x+1)^(1)/(3)dx is equal to :
  50. 50.The value of the integral _0^ /4xdx ^4(2x)+ ^4(2x) equals :