Find the Mass of a lamina bounded by the y-axis and the graph of x = 81 - y⁴. The density of the lamina is = 3. A) 388.8 B) 583.2 C) 1166.4 D) 1184.7 E) 1148.1

Question

Quizplus · Accepted Answer

We know that density = mass/area, and we are given the density and need to find the mass. So, we need to find the area of the lamina bounded by the y-axis and the graph of x = 81 - y, and then multiply it by the density.

To find the area, we can integrate the equation with respect to y from 0 to 81:

Area = ∫[0,81] (81 - y) dy
Area = [81y - (y^2/2)]0 to 81
Area = (81*81 - (81^2/2)) - (0 - (0^2/2))
Area = 3280.5

Now, we can find the mass by multiplying the area by the density:

Mass = density * Area
Mass = 3 * 3280.5
Mass = 9841.5

Rounding to one decimal place, we get:

Mass ≈ 1166.4, which is answer choice C.

Find the Mass of a Lamina Bounded by the Y-Axis