Rectangle areas are found by calculating height x width. The width of each rectangle equals Ax and the height of each rectangle is given by the function value at the right-hand side of the rectangle.
Rectangle areas are found by calculating height x width. The width of each rectangle equals Ax and the height of each rectangle is given by the function value at the right-hand side of the rectangle.
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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Question
5.1 q2
![Part (a)
Estimate the area under the graph of f(x) = cos(x) from x = 0 to x = π/2. Use four approximating rectangles and right endpoints. Is your estimate an underestimate or an overestimate?
Step 1 of 4
Rectangle areas are found by calculating height x width.
The width of each rectangle equals Ax and the height of each rectangle is given by the function value at the right-hand side of the rectangle.
So we must calculate R4 =
Since we wish to estimate the area over the interval [0, using 4 rectangles of equal widths, then each rectangle will have width 4x =
Step 2 of 4
We wish to find R4 = [f(x1) + f(x₂) + f(X3) + f(x4)]
<4)](T).
Since X1, X2, X3, X4 represent the right-hand endpoints of the four sub-intervals of [0,
Submit
X1 =
f(xi) Ax = [f(x₁) + f(x₂) + f(x3) + f(x4)] Ax, where x₁, X2, x3, x4 represent the right-hand endpoints of four equal sub-intervals of
[0].
i = 1
x2 =
x3 =
X4 =
Skip (you cannot come back)
then we must have the following.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d092c24-9208-441c-ac14-c31999d6a035%2Fb7ff9d79-b325-4d9b-85c8-78a476badb86%2Ftk3u1vm_processed.png&w=3840&q=75)
Transcribed Image Text:Part (a)
Estimate the area under the graph of f(x) = cos(x) from x = 0 to x = π/2. Use four approximating rectangles and right endpoints. Is your estimate an underestimate or an overestimate?
Step 1 of 4
Rectangle areas are found by calculating height x width.
The width of each rectangle equals Ax and the height of each rectangle is given by the function value at the right-hand side of the rectangle.
So we must calculate R4 =
Since we wish to estimate the area over the interval [0, using 4 rectangles of equal widths, then each rectangle will have width 4x =
Step 2 of 4
We wish to find R4 = [f(x1) + f(x₂) + f(X3) + f(x4)]
<4)](T).
Since X1, X2, X3, X4 represent the right-hand endpoints of the four sub-intervals of [0,
Submit
X1 =
f(xi) Ax = [f(x₁) + f(x₂) + f(x3) + f(x4)] Ax, where x₁, X2, x3, x4 represent the right-hand endpoints of four equal sub-intervals of
[0].
i = 1
x2 =
x3 =
X4 =
Skip (you cannot come back)
then we must have the following.
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