While the integral fills an area with an infinite number of rectangles and sums the areas to get
an exact area under a curve, there are many methods for finding an approximate area under a curve
as well. We will look at
Name_Melissa R Rauh_
Week 2 Topics: Trigonometric Identities and powers of trigonometric functions, inverse trigonometric
functions, integration by parts, trigonometric substitution, Partial Fraction decomposition, and
integration using ta
How to Approximate Area with the Trapezoid Rule:
With the trapezoid rule, instead of approximating area by using rectangles (for
example, as you do with the left and right sum methods), you approximate area
with can you guess? Trapezoids.
Because of the w
Integral Simpson's Rule:
This modified Riemann sum is Simpson's approximation to the definite integral.
For a continuous function f on [a, b], Simpson's approximation approaches the
definite integral (area).
Note the sequence of coefficients,cfw_ 1, 4, 2,
Integrals of Trigonometric Functions
Recall from the definition of an antiderivative that, if
f(x) = g(x),
g(x) dx = f(x) + C.
That is, every time we have a differentiation formula, we get an integration formula for nothing.
Here is a list of so