READ_ONLY_ACCESS
[
  {
    "id": "maths1-w09-000",
    "front": "Fundamental Theorem of Calculus (Part 1)",
    "back": "$\\frac{d}{dx} \\left[\\int_a^x f(t) dt\\right] = f(x)$"
  },
  {
    "id": "maths1-w09-001",
    "front": "Fundamental Theorem of Calculus (Part 2)",
    "back": "$\\int_a^b f(x) dx = F(b) - F(a)$, where $F'(x) = f(x)$"
  },
  {
    "id": "maths1-w09-002",
    "front": "Power rule for integration $\\int x^n dx$ ($n \\neq -1$)",
    "back": "$\\frac{x^{n+1}}{n+1} + C$"
  },
  {
    "id": "maths1-w09-003",
    "front": "Indefinite integral $\\int \\frac{1}{x} dx$",
    "back": "$\\ln|x| + C$"
  },
  {
    "id": "maths1-w09-004",
    "front": "Indefinite integral $\\int e^{kx} dx$",
    "back": "$\\frac{1}{k} e^{kx} + C$"
  },
  {
    "id": "maths1-w09-005",
    "front": "Geometric meaning of $\\int_a^b f(x) dx$",
    "back": "Net signed area between curve $y = f(x)$ and x-axis"
  },
  {
    "id": "maths1-w09-006",
    "front": "u-substitution is the integral counterpart of",
    "back": "The Chain Rule in differentiation"
  }
]