00:02
In this problem, we want to find the x and y coordinates of the centroid.
00:07
So the x coordinate of our centroid is given by the integral of x da over the area.
00:19
Similarly, the y coordinate is given by the integral of y da over our area.
00:25
So let's first find the area.
00:28
This will be given by the integral of the square root of x dx for x ranging between 0 and 6.
00:38
And we obtain x to the power of 3 halves over 3 halves for x ranging between 0 and 6, yielding 2 thirds times 6 to the power of 3 halves.
01:11
And from here, there's not much we can do to simplify our expression.
01:20
So let's provide a decimal format.
01:28
And we find 9 .8.
01:43
Now, let's evaluate this top integral.
01:48
I'm just writing ix for the integral.
01:51
And i'm putting a lot to be confused with in physics, inertia along the x coordinate.
01:57
It.
01:58
So we want to be integrating x times the double integral of x dx dy, where x will range between 0 and 6, and y will range between 0 and d squared root of x...