Description
Computer Assisted Questions:
4. Consider
Z 2
1
1
x
dx.
a) Use Riemann’s Left Hand Rule, Riemann’s Right Hand Rule, Riemann’s Midpoint Rule,
the Trapezoid Rule, Simpson’s Rule, and Boole’s rule to approximate the integral.
b) Compute the relative error in each case.
5. Consider
Z π
0
sin(x) + cos(x)dx.
a) Use the composite Trapezoid rule with n = 2, 10, 100, and 1000 intervals to approximate
the integral. Compute the relative error in each case.
b) Use the composite Simpson’s rule with n = 1, 5, 50, 500 and 5000 intervals to approximate
the integral. Compute the relative error in each case.
6. Use adaptive quadrature to approximate
1
√
2π
Z 1
−1
e
− x
2
2 dx
to 4 significant digits.