Question Solved1 Answer 8 We want to estimate the area under the curve y = x3 between r = 1 and x = 2. One way to do this is to construct rectangles under the curve, as shown on the right. The top left-hand corner of each rectangle touches the curve, and the width of each rectangle is given by Ax = 0.2. y =23 1 1 1.2 1.4 1.6 1.8 2 (a) Use the graph as shown to provide an estimate for the area under y = x3 between x = 1 and = 2. (b) Using Desmos, construct five rectangles of width Ar = 0.2 between x = 1 and x = 2. The top right-hand corner of each rectangle should touch the curve y = X. Use your graph to provide an estimate of the area under y = 23 between x = 1 to x = 2 (include the graph as part of your answer). (c) Use integration to evaluate the true area under the curve between x = 1 and x = 2, and compare this with the results from parts (a) and (b) above. Discuss your findings. (d) Suggest a way in which the accuracy of the methods used in parts (a) and (b) may be improved.

VCDOVQ The Asker · Calculus

Transcribed Image Text: 8 We want to estimate the area under the curve y = x3 between r = 1 and x = 2. One way to do this is to construct rectangles under the curve, as shown on the right. The top left-hand corner of each rectangle touches the curve, and the width of each rectangle is given by Ax = 0.2. y =23 1 1 1.2 1.4 1.6 1.8 2 (a) Use the graph as shown to provide an estimate for the area under y = x3 between x = 1 and = 2. (b) Using Desmos, construct five rectangles of width Ar = 0.2 between x = 1 and x = 2. The top right-hand corner of each rectangle should touch the curve y = X. Use your graph to provide an estimate of the area under y = 23 between x = 1 to x = 2 (include the graph as part of your answer). (c) Use integration to evaluate the true area under the curve between x = 1 and x = 2, and compare this with the results from parts (a) and (b) above. Discuss your findings. (d) Suggest a way in which the accuracy of the methods used in parts (a) and (b) may be improved.
More
Transcribed Image Text: 8 We want to estimate the area under the curve y = x3 between r = 1 and x = 2. One way to do this is to construct rectangles under the curve, as shown on the right. The top left-hand corner of each rectangle touches the curve, and the width of each rectangle is given by Ax = 0.2. y =23 1 1 1.2 1.4 1.6 1.8 2 (a) Use the graph as shown to provide an estimate for the area under y = x3 between x = 1 and = 2. (b) Using Desmos, construct five rectangles of width Ar = 0.2 between x = 1 and x = 2. The top right-hand corner of each rectangle should touch the curve y = X. Use your graph to provide an estimate of the area under y = 23 between x = 1 to x = 2 (include the graph as part of your answer). (c) Use integration to evaluate the true area under the curve between x = 1 and x = 2, and compare this with the results from parts (a) and (b) above. Discuss your findings. (d) Suggest a way in which the accuracy of the methods used in parts (a) and (b) may be improved.
See Answer
Add Answer +20 Points
Community Answer
7YOJBE The First Answerer
See all the answers with 1 Unlock
Get 4 Free Unlocks by registration

{:[y=x^(3)],[x=1quad x=2],[Delta x=0.2],[[1.1.2","1.4","1.6","1.8","2.0]],[int_(1)^(2)f(x)dx=Delta x[f(1)+f(1.2)+f(1.4)+f(1.6)+f(1.8)]],[=0.2[(1)^(3)+(1.2)^(3)+(1. ... See the full answer