Calculus I (AB) and Calculus II (BC): Trapezoidal Rule Application
If a 100-foot lake's width is measured at 10-foot intervals (as shown below), approximate the area of the lake using the Trapezoidal Rule:
Difficulty:
Calculus I (AB) and Calculus II (BC): Trapezoidal Rule Application
If a 100-foot lake's width is measured at 10-foot intervals (as shown below), approximate the area of the lake using the Trapezoidal Rule:
Difficulty:
Solution:Remember that the lake measures 0 feet across at its far left and right edges. When you apply the Trapezoidal Rule, don't fret about the shape of the lake and that it has a curvy bottom. (Much as the shape of my fat-infused curvy bottom doesn't bother me all that much.) Just treat this as if it were any old Trapezoidal Rule problem, multiplying all the non-endpoint function values by 2. This problem is actually very easy, because there's no function to plug into! All you have are function values, and all that's left is the calculatin'. One question: What are the a and b values? Well, if the lake is 100 feet long, we can set a = 0 and b = 100; of course, we're using 10 trapezoids (you can count them in the picture if you'd like) so n = 10:
| Home | Problem | Fun Calculus Stuff | Kelley's Books | Superbowl of Calculus |
