AP Calculus

Integrals:

Trapezoids

Definition = geometric shape a total of four sides, at least two of the sides must be parallel

Find The Area of a Trapezoid:

Equation = (Trapezoid Area) http://math.about.com/library/blmeasurement.htm

-Use this site as reference to b1, b2, and height: 

http://illuminations.nctm.org/Lessons/AreaForms/Trapezoid3.jpg

Why Are Trapezoids Important?:

-One can use trapezoids to determine a fairly accurate definite integral.

(definite integral = space underneath function line or curve that represents the product of x & y)

-Example of how to draw trapezoids within integral here:

http://www.peterstone.name/Maplepgs/images/Trapezoid_rule.gif

-Once the trapezoids have been drawn within the integral their areas are added to find the total.

-The more trapezoids drawn (the smaller the h, or change in x) the more accurate the integral.

Alternative Ways To Calculate Integral:

-Rather than adding each individual trapezoid’s area to find the total integral, this equation can be used: (1/2) x (h) x (b1 + 2b2 + 2b3 + 1b4) = total integral area

-This web site demonstrates b1, b2, b3, b4, and b5 but represents these sides as y1, y2, y3, y4, and y5:http://www.intmath.com/Integration/Tr1.gif

Finding Integral Using a Calculator:

            -Enter the function into the first Y= equation bar.

            -Enter L as the lowest side of the first trapezoid, or b1.

            -Enter U as the highest side of last trapezoid.

            -Enter N as the number of trapezoids within the integral.

            -Press Enter a final time for the calculator to give you the total integral.

HW: Page 18 #10 & #11, Page 21 All Quickies & #1-5 odd & #9-17 odd