8. The function f(x) = e² has an antiderivative, but there is no nice way to express it using elementary functions. Let's use Geogebra CAS to find the definite integral a) Use the command Integral(Function,Start x-Value,End r-Value). b) Approximate the area with 8, 16, 100, and 1000 rectangles using representative points of your choosing (e.g., left endpoints, right endpoints, midpoints) and the command RectangleSum(Function,Start x-Value, End r-Value,Number of Rectan- gles, Position for rectangle start). (NOTE: The Position for rectangle start is 0 for left endpoints, 1 for right endpoints, and 0.5 for midpoints.) c) Compare the approximations found in (b) to the area found in (a). What happens as you increase the number of rectangles? Submit your response along with a screenshot of your calculations from (a) and (b).
8. The function f(x) = e² has an antiderivative, but there is no nice way to express it using elementary functions. Let's use Geogebra CAS to find the definite integral a) Use the command Integral(Function,Start x-Value,End r-Value). b) Approximate the area with 8, 16, 100, and 1000 rectangles using representative points of your choosing (e.g., left endpoints, right endpoints, midpoints) and the command RectangleSum(Function,Start x-Value, End r-Value,Number of Rectan- gles, Position for rectangle start). (NOTE: The Position for rectangle start is 0 for left endpoints, 1 for right endpoints, and 0.5 for midpoints.) c) Compare the approximations found in (b) to the area found in (a). What happens as you increase the number of rectangles? Submit your response along with a screenshot of your calculations from (a) and (b).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8* I need help with a calculus homework question
Transcribed Image Text:8. The function f(x) = e²* has an antiderivative, but there is no nice way to express it
using elementary functions. Let's use Geogebra CAS to find the definite integral
* d.r
a) Use the command Integral(Function,Start x-Value,End x-Value).
b) Approximate the area with 8, 16, 100, and 1000 rectangles using representative
points of your choosing (e.g., left endpoints, right endpoints, midpoints) and the
command RectangleSum(Function,Start x- Value, End x-Value,Number of Rectan-
gles, Position for rectangle start). (NOTE: The Position for rectangle start is 0
for left endpoints, 1 for right endpoints, and 0.5 for midpoints.)
c) Compare the approximations found in (b) to the area found in (a). What happens
as you increase the number of rectangles? Submit your response along with a
screenshot of your calculations from (a) and (b).
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