Question

b) Consider the region R with density $f(x, y) = xy$ in Figure 1 below: y 3 $x = y$ R $x = 6 - y$ 6 x [9 marks] Figure 1 i) Find the mass M of the region R ii) Find the center of mass ($\bar{x}$, $\bar{y}$) of the region R Hint: $M = \iint_R f(x, y) dxdy$, $\bar{x} = \iint_R xf(x, y) dxdy$, $\bar{y} = \iint_R yf(x, y) dxdy$

          b) Consider the region R with density $f(x, y) = xy$ in Figure 1 below:

y
3
$x = y$
R
$x = 6 - y$
6
x
[9 marks]
Figure 1
i) Find the mass M of the region R
ii) Find the center of mass ($\bar{x}$, $\bar{y}$) of the region R
Hint: $M = \iint_R f(x, y) dxdy$, $\bar{x} = \iint_R xf(x, y) dxdy$, $\bar{y} = \iint_R yf(x, y) dxdy$

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b) Consider the region R with density f(x, y) = xy in Figure 1 below:

y
3
x = y
R
x = 6 - y
6
x
[9 marks]
Figure 1
i) Find the mass M of the region R
ii) Find the center of mass (x̅, y̅) of the region R
Hint: M = f(x, y) dxdy, x̅ = xf(x, y) dxdy, y̅ = yf(x, y) dxdy

Added by Matthew B.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Sri K

12/08/2022

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