Evaluate the integral $I = \int_0^3 x^3 \, dx$ using the Trapezoidal rule with step size $h = 1$. What is the numerical value obtained?

Answer Key:

22.5

### Solution: Grid points $x = 0, 1, 2, 3$ with $f(x) = 0, 1, 8, 27$. Trapezoidal rule: $I = \frac{h}{2}[f_0 + 2(f_1 + f_2) + f_3] = \frac{1}{2}[0 + 2(1 + 8) + 27] = \frac{1}{2}[18 + 27] = \frac{45}{2} = 22.5$. Correct: 22.5.

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