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Let T2be triangular region with vertices (1,0),(2,1), and(2,-1)

If the density at each point in T2is proportional to the square of the point’s distance from the y-axis, find the mass of T2.

Short Answer

Expert verified

The mass of lamina ism=176k.

Step by step solution

01

Given Information

Vertices of triangular region is(1,0),(2,1),and(2,-1)

02

Calculating Mass of Lamina

Formula is m=Ωρ(x,y)dA

Also density is ρ(x,y)=kx2

m=12-x+1x-1kx2dydx

Solving inner integral first

m=12kx2[y]-x+1x-1dx

m=12kx2[x-1-(-x+1)]dx

m=2k12x3-x2dx

m=2kx44-x3312

Putting limits

m=2k244-233-14-13

m=2k1712

Hence,m=176k

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