Question

Find the center of mass of the planar lamina bounded by y = a - x2 (a > 0) and the x-axis, assuming a mass density ρ(x, y) = y.

Name: find the center of mass of the planar lamina bounded by y a x2 a 0 and the x axis assuming a mass density x y y 33792
Uploaded: 2022-11-14T13:07:41-08:00
Duration: 4 min 23 s
Channel: Adi S
Description: find the center of mass of the planar lamina bounded by y a x2 a 0 and the x axis assuming a mass density x y y 33792

          Find the center of mass of the planar lamina bounded by y = a -
x2 (a > 0) and the x-axis, assuming a mass
density ρ(x, y) = y.

Added by Elizabeth M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/14/2022

Step 1

Step 1: Calculate the mass, \( m \), of the lamina: \[ m = \iint\limits_{D} y \, dy \, dx \] \[ m = \int_{0}^{\sqrt{a}} \int_{0}^{a-x^2} y \, dy \, dx \] \[ m = \int_{0}^{\sqrt{a}} \left[ \frac{y^2}{2} \right]_{0}^{a-x^2} \, dx \] \[ m = \int_{0}^{\sqrt{a}} Show more…

Show all steps