Approximate the area of the region beneath the graph of h(x) = 4xe* from x=0 to x = 4, using (1) four left rectangles (ii) four right rectangles (iii) four midpoint rectangles. (a) In each case, on a graph of h from x = 0 to x = 4 mark and label appropriate subintervals along the x-axis and draw the rectangles. (1) graph of left-rectangle approximation h(x) 1 h(x) 1 2 3 4 O h(x) 1 h(x) 1 2 3 4

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Approximate the area of the region beneath the graph of h(x) = 4xe* from x = 0 to x = 4, using
(1) four left rectangles
(ii) four right rectangles.
(iii) four midpoint rectangles.
(a) In each case, on a graph of h from x = 0 to x = 4 mark and label appropriate subintervals along the x-axis and draw the rectangles.
(1) graph of left-rectangle approximation
O
h(x)
(ii) graph of right-rectangle approximation
h(x)
h(x)
1
2
h(x)
1
2
MA
2
O left-rectangle approximation
O midpoint-rectangle approximation
3
(iii) graph of midpoint-rectangle approximation
h(x)
3
2
2
3
3
3
O
3
4
INA
O
h(x)
O
Calculate the approximate areas. (Round your answer to three decimal places.)
left-rectangle approximation
right-rectangle approximation
midpoint-rectangle approximation
h(x)
h(x)
H(X)
1
h(x)
2
1
3
2
3
3
3
(b) The actual area, to nine decimal places, of the region beneath the graph of h(x) = 4xe, is 3.633687222. Which of the approximations found in part (a) is the most accurate?
O right-rectangle approximation
Transcribed Image Text:Approximate the area of the region beneath the graph of h(x) = 4xe* from x = 0 to x = 4, using (1) four left rectangles (ii) four right rectangles. (iii) four midpoint rectangles. (a) In each case, on a graph of h from x = 0 to x = 4 mark and label appropriate subintervals along the x-axis and draw the rectangles. (1) graph of left-rectangle approximation O h(x) (ii) graph of right-rectangle approximation h(x) h(x) 1 2 h(x) 1 2 MA 2 O left-rectangle approximation O midpoint-rectangle approximation 3 (iii) graph of midpoint-rectangle approximation h(x) 3 2 2 3 3 3 O 3 4 INA O h(x) O Calculate the approximate areas. (Round your answer to three decimal places.) left-rectangle approximation right-rectangle approximation midpoint-rectangle approximation h(x) h(x) H(X) 1 h(x) 2 1 3 2 3 3 3 (b) The actual area, to nine decimal places, of the region beneath the graph of h(x) = 4xe, is 3.633687222. Which of the approximations found in part (a) is the most accurate? O right-rectangle approximation
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