# I Calculating total force over bounded area [Given p density]

1. Apr 8, 2016

### NZBRU

Hey, I am trying to prove that taking a 'horizontal' and 'vertical' strip equates to the same answer for the following problem. I have the current solution for taking a horizontal strip (ie dA = dxdy) and letting the bounds of x be between the two equations x(y) and the bounds of y be between zero and -1/2.

What I am trying to accomplish is to set up the integration differently to yield the same result (to aid in my conceptual understanding). From my understanding the below integral should be 'equivalent' as dy is integrated between the two bounded equations and x is bounded between 1 and -2:

However this integral evaluates to 27pg/32 which is obviously incorrect. I was wondering if anyone could help me with my approach/logic. The solution using the textbooks method is below:

Cheers.

2. Apr 13, 2016