An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it on display. The artwork has constant density and must be balanced at its centroid. The shape of the artwork was created on a computer program then casted and fabricated. The following equation was put into the computer to generate the shape:

$\displaystyle {y}={1}{\sin{{\left(\pi{x}\right)}}}+{5}$ bounded by x = 0, x = 2, and y = 0

Draw the Lamina in an x-y plane and put a dot where the centroid should be. Show all work and formulas you are using.

The centroid is at $\displaystyle {\left(\overline{{x}},\overline{{y}}\right)}$, where

$\displaystyle \overline{{x}}$ = Preview Question 6 Part 1 of 2  

$\displaystyle \overline{{y}}$ = Preview Question 6 Part 2 of 2