Please list out in detail the process I dont want an answer

Please list out in detail the process. I don\'t want an answer, but rather I want to see a step-by-step description of how this problem is done so I can see where I am going wrong on my math. Thank you so much and the answer from the answer key is:

Solution

We need to divide the triangle into strips.
If x is the distance from the upper vertex of the triangle to the strip the area of the strip is 2/3 dx and the pressure on the strip is 62.5 (15+x) (We use the fact that the ratio of the sides of a 30-60-90 triangle are 1:3:2)

We add up all the strips from 0 to 3 the height of the triangle and get

int 62.5 (15 +x)* 2/3 x dx from 0 to 3

int 62.5 (30/3 x + 2/3 x^2) dx

Antiderivative is

62.5(15/3 x^2 + 2/33 x^3)

Evaluating this from 0 to 3 we get

62.5 (15 +2/3 3)3