Definite Integrals

• the definite integral over the interval [𝑎,𝑏] is a limit of Riemann sums:
  • $\underset{\text{Definite Integral}}{\underbrace{{\int }_a^{b}f(x)dx}}={\lim }_{n\to \infty }\underset{\text{Riemann Sums}}{\underbrace{\sum _{i=1}^{n}f(x_i)𝛥x}}$
• where:
  • 𝑥_𝑖 = 𝑎 + 𝑖·(𝛥𝑥)
  • 𝛥𝑥 = (𝑏 - 𝑎) / 𝑛