Question

#4 Points possible: 1. Total attempts: 6 A thin metal plate is shaped like a semicircle of radius 12 meters in the right half-plane, centered at the origin. The area density of the metal only depends on e, and is given by measured in meters and p(a) measured in kg/m2. The density is measured at a few locations in the plate, as given below: an unknown function p(x), with a 9 12 0 3 6 P(x) 2.9 2 2.7 2.5 Use Simpson's Rule to approximate the total mass of the plate. Hint: Set up an integral for the mass in terms of p(ar) first. Use Simpson's Rule to approximate this integral. kg

Answer 1

here h=(0+12)/4

h=3

from simpson"s rule

h/3[(y₀+y_n)+4(y₁+y₃.....)+2(y₂+y₄.....)]

putting the given values

3/3[(2+2.7)+4(2.5+2)+2*2.9]=28.5