Lesson #134
Numerical Methods
of Integration
Quote of the Day:
"On the other hand, it is impossible for a cube to be
written as a sum of two cubes or a fourth power to be
written as a sum of two fourth powers or, in general for
any number which is a power greater than the second to
be written as a sum of two like powers. For this I have
discovered a truly wonderful proof, but the margin is
too small to contain it." -- P. Fermat
Objectives:
The student will use the trapezoidal rule to approximate a
definite integral.
The student will use Simpson's rule to approximate a
definite integral
1. Collect homework.
2. Recall that when we first began the study of integrals,
we used Riemann sums with rectangles to approximate the
area under a curve. Now we will look at two other
methods of approximating the area under the curve.
(a) Trapezoidal Rule
Approximate the area using trapezoids:
(b) Simpson's Rule
Based on a formula to find area under parabolic arc:
3. Examples
