Question

Find the centre of mass of the given region y=x^2 and y=x if the density is x+1​

Answer 1

Given:

Region y=x^2 and y=x

Density is x+1​

To find:

Centre of mass of the given region

Answer:

• Area of the region emcompassed by y=x² and y=x is A = x² - x
• Center of mass of the section is given by:
• $m = \int\limits^a_b {(density * area)} \, dx$
• $m = \int\limits^1_0 {(x+1) * (x -x^{2} )} \, dx$
• $m = \int\limits^1_0 {(-x^{3} + x) } \ dx$
• m = $\left \{ {{x=1} \atop {x=0}} \right. \frac{-x^{4} }{4} + \frac{x^{2} }{2}$
• m = 1/2 - 1/4
• m = 1/4