87.2k views
5 votes
A solid of revolution is formed by rotating about the x-axis, the area q8Letween the x-axis, the lines x = 0 and x = 1 and a curve through the points with the following co-ordinates : 0.00 0.25 0.50 .0.75 1.00 1.0000 0.9896 0.9589 0.9089 0.8415 Estimate the volume of the solid formed using Simpson's rule. y :

User BenA
by
7.8k points

1 Answer

4 votes

Final answer:

To estimate the volume of the solid formed by rotating the curve about the x-axis, we can use Simpson's rule. Simpson's rule involves dividing the interval into subintervals, calculating function values, and applying a weighted average formula. Finally, multiply the estimated area by the width of the interval to get the estimated volume.

Step-by-step explanation:

Simpson's rule is a numerical method used to estimate the area under a curve. To estimate the volume of the solid formed by rotating the curve about the x-axis, we can use Simpson's rule to estimate the area between the curve and the x-axis. Here's how:

  1. Divide the interval [0, 1] into an even number of subintervals. In this case, we have 5 subintervals.
  2. Calculate the width of each subinterval, which is the difference between consecutive x-values: h = (1-0)/5 = 0.2
  3. Calculate the function values at each x-coordinate using the given points.
  4. Apply Simpson's rule to estimate the area. I won't go into the details here, but the formula involves adding up a weighted average of the function values.
  5. Finally, multiply the estimated area by the width of the interval to get the estimated volume of the solid formed.
User Morozov
by
8.1k points