4.2/4.3 Area, Riemann Sums and Definite Integrals
Consider the region bounded by the graphs of and . The area of the region can be approximated
by two sets of rectangles one set inscribed within the region and the other set circumscribed
over the region.
4.6 Numerical Integration
Approximating a definite integral using the Trapezoidal and Simpsons Rule
Some elementary functions simply do not have antiderivatives that are elementary functions. Ex:
If you need to evaluate a definite integra
4.5 Integration by Substitution
In this section, we will look at techniques for integrating composite functions. The technique
used is much the same as the substitution used when differentiating composite functions. As in
differentiation, we let be our in
6.3 Separation of Variables
In the last section we saw that in some differential equations all the x terms can be collected with
dx and all the y terms with dy, and a solution can be obtained by integration. Such equations are
said to be separable, and th
Consider a function that is differentiable at . The equation for the tangent line at the point is given by
and is called the tangent line approximation (or linear approximation) of at .
Because is a constant, is a linear function of .
A slope field (or direction field) consists of line segments with slopes given by the differential
equation. These line segments give a visual perspective of the slopes of the solutions of the
a. Sketch two approximate