1-124.2 Riemann Sums103. Use a left Riemann sum with n = 4 subintervals to approximate the area under the curve f(x)=(0, 2). The graph of f(r) is below, illustrate the Riemann sums on this graph and state whethoverestimate or underestimate.643(v(1) / (√2 + 2)²5√//(1)√36(k) / T√√-362²8$1507531-f(x)da12I34 subintervals to approximate the area under04. Use a right Riemann sum with n[0, 2]. The graph of f(r) is below, illustrate the Riemann sums on this graph aoverestimate or underestimate.13

The given curve is, To Evaluate: Area under the curve using Left Riemann sum rule over the interval [0,2].Left Riemann sum: A=∑i=1nfxi∆x, where f(xi) is the value of the function at left end point of each sub-interval. Number of subintervals is 4. Length of each sub-interval is: ∆x=2-04=24=0.5. Sub-intervals are: 0,0.5,0.5,1,1,1.5,1.5,2. A=∑i=14fxi∆x=f0+f0.5+f1+f1.5×0.5=6+4.2+3.3+2.8×0.5=8.15 Approximated area under the curve is 8.15(approx). this function is decreasing and we have taken function value at left end point So, the area we obtained will be an overestimation.

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103. Use a left Riemann sum with n= 4 subintervals to approximate the area under the curve f(x (0, 2). The graph of f(z) is below, illustrate the Riemann sums on this graph and state whe overestimate or underestimate. [(*) 3 1 5 4 2 8 7 6 2 I 3

103. Use a left Riemann sum with n= 4 subintervals to approximate the area under the curve f(x (0, 2). The graph of f(z) is below, illustrate the Riemann sums on this graph and state whe overestimate or underestimate. [(*) 3 1 5 4 2 8 7 6 2 I 3

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

1
-1
2
4.2 Riemann Sums
103. Use a left Riemann sum with n = 4 subintervals to approximate the area under the curve f(x)=
(0, 2). The graph of f(r) is below, illustrate the Riemann sums on this graph and state wheth
overestimate or underestimate.
6
4
3
(v
(1) / (√2 + 2)²
5√//
(1)
√36
(k) / T
√√-362²
8
$150
7
5
31
-
f(x)
da
1
2
I
3
4 subintervals to approximate the area under
04. Use a right Riemann sum with n
[0, 2]. The graph of f(r) is below, illustrate the Riemann sums on this graph a
overestimate or underestimate.
13

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