Question

Approximating With Simpson's Rule 6) Now we want to use Simpson's Rule to find the volume of the machine part. Remember that Simp- son's Rule approximates integrals, not just areas. Since we don't just want the area under the radius function, we can't just apply Simpson's Rule to the radius function. If we let f(x) be the radius of the machine part at the point x, write down the integral that gives the volume of the machine part (with an undetermined function fix). Typeset it nicely using the Palette (or keyboard shortcuts) fx] dx Oug -28.3947 17.6 r 2 To use Simpson's Rule, we need a list of the values for the function we want to integrate (not just fix), which just describes the radius), and to do this in Mathematica, we need a new command: /@(called "slash-at). The command g/@pts applies the function g to each element of the list pts. For example, try this code: clear [a, b, c, d, e] pts (a, b, c, d, e g[x]7+x^ 17 Ings g /e pts Ougs(a, b, c, d, e) Ou (7- a", 7. b, 7.c", 7 . di", 7- el') 7) Use /@ to create a new list of points that represent the values of the function we need to find the volume of the machine part. Call this list volPts. integrate to Volume of Intersecting Cylinders Project.nb 10 volPts (4.2, 3.8, 4.2, 4.7, 5.2, 5.7, 5.8, 5.4, 4.9, 4.4, 4.6) f /e volPts Ouero(4.2, 3.8, 4.2, 4.7, 5.2, 5.7, 5.8, 5.4, 4.9, 4.4, 4.6) Our (f4.2], f(3.8), f(4.21. f(4.71, f(5.21. f5.7, f5.8], f(5.4], f(4.9], f(4.4], f4.6]} 8) Copy and paste the code for your simpson[ ] function from the "Income Inequality" project earlier in the quarter. Then use your simpson[] function to approximate the volume of the machine part. Hint: Your volume should be about 598 cm2. If you didn't get this, you are doing something wrong, and should fix it before you turn in your assignment

Answer 1

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