Question

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 :

Answer 1

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.