Please help NO LINKS 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:

y
=
4
sin
(
π
x
)
+
6
y
=
4
sin
(
π
x
)
+
6
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
(
¯
x
,
¯
y
)
(
x
¯
,
y
¯
)
, where

¯
x
x
¯
=

¯
y
y
¯
=