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 = (x) 4x = [1(x₁) + 1(×₂) + 1(×3) + √(x4)]ax, where X₁, X2, X3, X4 represent the midpoints of four equal sub-intervals of [0, 2]. 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 1/2. Part 2 of 3 We wish to find M₁ = ()[(1) + f(×2) + √(×3) + f(x4)]· (±)[1(×1) M4 Since X₁, X₂, X3, x4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X1 X₂ IX IX X3 11 = =
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 = (x) 4x = [1(x₁) + 1(×₂) + 1(×3) + √(x4)]ax, where X₁, X2, X3, X4 represent the midpoints of four equal sub-intervals of [0, 2]. 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 1/2. Part 2 of 3 We wish to find M₁ = ()[(1) + f(×2) + √(×3) + f(x4)]· (±)[1(×1) M4 Since X₁, X₂, X3, x4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following. X1 X₂ IX IX X3 11 = =
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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5.2 q2
![Tutorial Exercise
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 = √(x)µ× = [f(x1) + f(x₂) + √(×3) + f(x4)]4x, where X1, X2, X3, X4 represent the
i = 1
midpoints of four equal sub-intervals of [0, 2].
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
1/2
Part 2 of 3
We wish to find M₁ = ( ) [√(x1) + √(×₂) + √(×3) + f(x4)].
M4
Since X₁, X₂, X3, X4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following.
X₁
=
x₂ =
x3 =
X4 =
111
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Transcribed Image Text:Tutorial Exercise
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 = √(x)µ× = [f(x1) + f(x₂) + √(×3) + f(x4)]4x, where X1, X2, X3, X4 represent the
i = 1
midpoints of four equal sub-intervals of [0, 2].
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
1/2
Part 2 of 3
We wish to find M₁ = ( ) [√(x1) + √(×₂) + √(×3) + f(x4)].
M4
Since X₁, X₂, X3, X4 represent the midpoints of the four sub-intervals of [0, 2], then we must have the following.
X₁
=
x₂ =
x3 =
X4 =
111
Submit Skip_(you cannot come back)
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