Question

Find the exact coordinates of the centroid.

Answer 1

\[y = e^x, y=0, x = 0, x =5\]

Answer 2

\[A = \int\limits_{0}^{5}e^xdx = [e^x]_{0}^{5}= e^5-1\]\[x = \frac{ 1 }{ A }\int\limits_{a}^{b}xe^xdx=\frac{ 1 }{ e^5-1 }[xe^x-e^x]_{0}^{5}\]\[\frac{ 1 }{ e^5-1 }[(5e^5-e^5)-(0-1)]\]\[\frac{ 1 }{ e^5-1 }[5e^5-e^5+1]\]

Am I doing it correctly so far?

Answer 3

looks good so far :)

Answer 4

@Zenmo
You have completed (correctly) the calculation of X_bar.
But recall that Y_bar is the second part of the answer!
You will be integrating \(\int_0^5 (y/2)*ydx\) where y=e^x, and y/2 is the y-distance from the x-axis of the centroid of the strip.