Consider the given function. f(x) = c +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints. Part 1 of 3 We must calculate M4= Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax= -1/2 X Part 2 of 3 We wish to find M4= x₂ = Since X₁, X₂, x3, x4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X1 0.25 1/4 x3 X4 = · Ĺ ‹(ׂ)µ× = [r(×₁) + f(×₂) + √(×3) + f(xa)]µ×, where X₁, X₂, X3, X4 represent the midpoints of four equal sub-intervals of [0, 2]. /=1 = (±)[^(×₁) + f(×₂) + √(×3) + f(×4)] · M4 = 0.75 ✔ 1.25 1.75✔ 3/4 5/4 7/4 Part 3 of 3 Using f(x) = ex + 8, we have the following. · ( ² ) [( ₁ + ₁) + (² + •)· ( √ - · 8) + (∞— + 8) + ( ∞ — + s)] (rounded to six decimal places) 1/2.
Consider the given function. f(x) = c +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints. Part 1 of 3 We must calculate M4= Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax= -1/2 X Part 2 of 3 We wish to find M4= x₂ = Since X₁, X₂, x3, x4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X1 0.25 1/4 x3 X4 = · Ĺ ‹(ׂ)µ× = [r(×₁) + f(×₂) + √(×3) + f(xa)]µ×, where X₁, X₂, X3, X4 represent the midpoints of four equal sub-intervals of [0, 2]. /=1 = (±)[^(×₁) + f(×₂) + √(×3) + f(×4)] · M4 = 0.75 ✔ 1.25 1.75✔ 3/4 5/4 7/4 Part 3 of 3 Using f(x) = ex + 8, we have the following. · ( ² ) [( ₁ + ₁) + (² + •)· ( √ - · 8) + (∞— + 8) + ( ∞ — + s)] (rounded to six decimal places) 1/2.
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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![Tutorial Exercise
Consider the given function.
f(x) = e² +8
Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints.
Part 1 of 3
We must calculate M₁ =
Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax = -1/2 X
- Σ ‹(×;)µ× = [√(x1) + √(×2) + √(×3) + f(xa)]µ×, where X₁, X2, X3 X4 represent the midpoints of four equal sub-intervals of [0, 2].
Part 2 of 3
We wish to find M4 = (¹)[(1) + t(×2) + f(×3) + f(×4)]·
Since X₁, X2, X3, X4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following.
X₁ = 0.25✔✔
1/4
X2 = 0.75 ✔✔
x3 = 1.25 ✔
X4 =
1.75 ✔
3/4
5/4
7/4
Part 3 of 3
Using f(x) = ex + 8, we have the following.
M₁ - (+)(d
M4
+8
³+ 8) + (₁+3)+(₁+3)]
(rounded to six decimal places)
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Transcribed Image Text:Tutorial Exercise
Consider the given function.
f(x) = e² +8
Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct to six decimal places, taking the sample points to be midpoints.
Part 1 of 3
We must calculate M₁ =
Since we wish to estimate the area over the interval [0, 2] using 4 rectangles of equal widths, then each rectangle will have width Ax = -1/2 X
- Σ ‹(×;)µ× = [√(x1) + √(×2) + √(×3) + f(xa)]µ×, where X₁, X2, X3 X4 represent the midpoints of four equal sub-intervals of [0, 2].
Part 2 of 3
We wish to find M4 = (¹)[(1) + t(×2) + f(×3) + f(×4)]·
Since X₁, X2, X3, X4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following.
X₁ = 0.25✔✔
1/4
X2 = 0.75 ✔✔
x3 = 1.25 ✔
X4 =
1.75 ✔
3/4
5/4
7/4
Part 3 of 3
Using f(x) = ex + 8, we have the following.
M₁ - (+)(d
M4
+8
³+ 8) + (₁+3)+(₁+3)]
(rounded to six decimal places)
Submit Skip (you cannot come back)
1/2.
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