In this lesson, Professor John Zhu gives an introduction to the trapezoid rule. He defines the trapezoid rule and the area of a trapezois. He reviews the terms of the formula as well as works out several example problems.
Approximate the area under f(x) = 3x2 from x = 0 to x = 4 using 4 inscribed trapezoids.
Width of trapezoids = [(4 − 0)/4] = 1
A ≈ [1/2] [f(0) + 2f(1) + 2f(2) + 2f(3) + f(4)]
A ≈ [1/2] [0 + 6 + 24 + 54 + 48]
This is a property of even functions. If A1 is the area of an even function from −a to 0, and A2 is the area of the same even function from 0 to a, then A1 = A2
A ≈ 66
Approximate the area under f(x) = 3x2 from x = −4 to x = 4 using 8 inscribed trapezoids.
If the trapezoid widths were different, the same approximations found in the previous problems won't necessarily hold. But, this problem shares the same width as previous two problems. We can use the approximates previously found.
A ≈ 66 + 66
A ≈ 132
Approximate the area under f(x) = cosx from x = 0 to x = π using 4 inscribed trapezoids.
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.