Left and Right Rectangle Riemann Sums Approximate each of the given definite integrals using the specified method. You may leave your answers in expanded form (as a sum of products). Note that n represents the number of sub-intervals for each sum. Definite Integral f(x)dx [F(x)dx -32 -1 f(t)\ dt 0 for f(x) dx Method n = 3 Left Riemann Sum 1 2 3 4 n = 4 Right Riemann Sum Definite Integral Method 0 12 4 20 Given: The table below gives velocity values measured in ft/sec every 4 seconds. Time (seconds) 12 16 Velocity (ft/sec) -12 10 n4 Left Riemann sum n=3 Right Riemann sum 8 5 -8 6 7 8 9 Approximation Approximation 10 11 antal (2) dx

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Left and Right Rectangle Riemann Sums
Approximate each of the given definite integrals using the specified method. You may leave
your answers in expanded form (as a sum of products). Note that n represents the number of
sub-intervals for each sum.
Definite Integral
f(x) dx
[F(x)dx
-32 -1
f(t)\ dt
0
for f(x) dx
Method
n = 3 Left Riemann Sum
1 2 3 4
n = 4 Right Riemann Sum
Definite Integral Method
0
12
4
20
Given: The table below gives velocity values measured in ft/sec every 4 seconds.
Time (seconds)
12
16
Velocity (ft/sec)
-12
10
n4 Left Riemann
sum
n=3
Right Riemann sum
8
5
-8
6
7
8 9
Approximation
Approximation
10 11
dx
Transcribed Image Text:Left and Right Rectangle Riemann Sums Approximate each of the given definite integrals using the specified method. You may leave your answers in expanded form (as a sum of products). Note that n represents the number of sub-intervals for each sum. Definite Integral f(x) dx [F(x)dx -32 -1 f(t)\ dt 0 for f(x) dx Method n = 3 Left Riemann Sum 1 2 3 4 n = 4 Right Riemann Sum Definite Integral Method 0 12 4 20 Given: The table below gives velocity values measured in ft/sec every 4 seconds. Time (seconds) 12 16 Velocity (ft/sec) -12 10 n4 Left Riemann sum n=3 Right Riemann sum 8 5 -8 6 7 8 9 Approximation Approximation 10 11 dx
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