Approximating Area Given Data

Question

Let f(t) = sin(t^2). Use the trapezoidal rule with four equal subdivisions of the closed interval [0,1] to approximate area under the curve f on the interval [0,1]

Answer 1

Area A = ∫₀¹sin(t²)dt ≈ (1 - 0)/8(sin(0²) + 2sin(0,25²) + 2sin(0.5²) + 2sin(0.75²) + sin(1²)) = 0.3160

Answer 2