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Indefinite Integrals

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  1. 101.Let f:[0,2]R be defined as f(x) = casese^x^2,,x-[x], & x[0,1) e^[x-_ex], & x[1,2)cases, wh…
  2. 102.If f:RR is a continuous function satisfying _0^/2f(2x) x,dx+_0^/4f(2x) x,dx=0, then the va…
  3. 103.If _-0.15^0.15|100x^2-1|,dx = k3000, then k is equal to ______.
  4. 104.If _0^1dx(5+2x-2x^2)(1+e^2-4x) = 1_e(+1), ,>0, then ^4-^4 is equal to:
  5. 105.Let I(x) = (x^2x+ x)/((x x+1)^2),dx.
  6. 106.Let I(x) = ((x+1))/(x(1+xe^x)^2),dx, x>0.
  7. 107.The integral (x^x x^-x+2^x x^-x)_2 x,dx (as reconstructable from the source) is equal to:
  8. 108.If I(x) = e^^2x( x2x- x),dx and I(0)=1, then I(3) is equal to:
  9. 109.For ,,,N, if (x^e^2x+(e^x)/(2x))^!_e x,dx = 1 x^e^ x-1e^x x+C (reconstructed form), then +…
  10. 110._0^6e^3x+6e^2x+11e^x+6,dx equals:
  11. 111.Let f(x) = dx(3+4x^2)√4-3x^2, x<2√3.
  12. 112.The value of 12_0^3|x^2-3x+2|,dx is Answer: 22
  13. 113.If 1x(1-x)/(1+x),dx = g(x)+c, g(1)=0, then g(12) is equal to:
  14. 114.If ((x^2+1)e^x)/((x+1)^2),dx = f(x)e^x+C, where C is a constant, then d^3fdx^3 at x=1 is e…
  15. 115.The value of the integral _-/2^/2(dx)/((1+e^x)(^6x+^6x)) is equal to:
  16. 116._n_k=1^n(n^2)/((n^2+k^2)(n+k)) is equal to:
  17. 117.The value of _0^e^ x x(1+^2x)(e^ x+e^- x),dx is equal to:
  18. 118.Let g:(0,)R be a differentiable function such that [[(x( x- x))/(e^x+1)+(g(x)(e^x+1-xe^x))…
  19. 119.If b_n = _0^/2(2nx)/( x),dx, nN, then:
  20. 120.The value of b>3 for which 12_3^b(dx)/((x^2-1)(x^2-4)) = _e4940 is equal to Answer: 6
  21. 121.Let f(x)=|x+1|,|x+2|,,|x+5|.
  22. 122.The value of the integral 48_0^/4(a rational/trigonometric expression in x)dx is equal to …
  23. 123.The integral 24√2,(2-x^2),dx(2+x^2)√4+x^4 (over the source's stated limits) is equal to An…
  24. 124.The value of the integral _-2^2|x^3+x|e^x|x|+1,dx is equal to:
  25. 125.Let f be a differentiable function in (0,2).
  26. 126.The integral _0^117^[1/x],dx, where [] denotes the greatest integer function, is equal to
  27. 127.Let [t] denote the greatest integer less than or equal to t.
  28. 128.Let f:RR be a differentiable function such that f(4)=√2, f(2)=0 and f'(2)=1, and let g(x)=…
  29. 129.Let f:RR be a continuous function satisfying f(x)+f(x+k)=n for all xR, where k>0 and n is …
  30. 130._0^5((x-[x/2])),dx, where [t] denotes greatest integer less than or equal to t, is equal t…
  31. 131.Let f be a real valued continuous function on [0,1] and f(x) = x+_0^1(x-t)f(t),dt.
  32. 132.If _0^2√2x-x^2,dx = _0^1(1-√1-y^2-y^22)dy + _1^2(2-y^22)dy + I, then I equals:
  33. 133.Let f() = +_-/2^/2(+t)f(t),dt.
  34. 134.The integral (1-1√3)( x- x)1+2√32x,dx is equal to
  35. 135.For I(x) = ^2x-2022^2022x,dx, if I(4)=2^1011, then:
  36. 136.For any real number x, let [x] denote the largest integer less than or equal to x.
  37. 137._n12n[1√1-(12n)^2+1√1-(22n)^2++1√1-((2n-1)/(2n))^2] is equal to
  38. 138.Let [t] denote the greatest integer less than or equal to t.
  39. 139.Let a_n = _-1^n(1+x2+x^23++x^n-1n)dx for every nN.
  40. 140.If n(2n+1)_0^1(1-x^n)^2n,dx = 1177_0^1(1-x^n)^2n+1,dx, then nN is equal to ________.
  41. 141._0^20(| x|+| x|)^2,dx is equal to
  42. 142.Let f:RR be a function defined as f(x) = a[x]2+[2-x], aR, where [t] is the greatest intege…
  43. 143.Let f(x) = 2+|x|-|x-1|+|x+1|, xR.
  44. 144._0^2(|2x^2-3x|+[x-12]),dx, where [t] is the greatest integer function, is equal to:
  45. 145.Let f(x) = [x-1],[x-2],,[x-10], where [t] denotes the greatest integer t.
  46. 146.Let f be a differentiable function satisfying f(x) = 2√3_0^√3f!(^2/3x)d, x>0, and f(1)=√3.
  47. 147.If _0^√315x^3√1+x^2+(1+x^2)^3,dx = √2+√3 (reconstructed form), where , are integers, then …
  48. 148.Let I_n(x) = _0^x1(t^2+5)^n,dt, n=1,2,3,.
  49. 149.The value of the integral _0^/2(60(6x))/( x),dx is equal to________.
  50. 150.The integral _0^/213+2 x+ x,dx is equal to: