3. Consider the integral $\int_1^4 \ln x \, dx$.
(a) Approximate the integral using Gaussian quadrature with 3 nodes/weights. Use the
Gauss nodes and weights given in the textbook. Give your final answer to three
decimal places.
(b) Given that $\int \ln x \, dx = x \ln x - x + C$, what is the actual error in your answer?
4. Repeat Problem 2 above, but use the Trapezoid method with 3 equally spaced nodes (use
$x_0 = 1$, $x_1 = 2.5$, $x_2 = 4$). What is the error?
5. Repeat Problem 2 above, but use Simpson's method with 3 equally spaced nodes (use
$x_0 = 1$, $x_1 = 2.5$, $x_2 = 4$). What is the error?
