# Thread: Help with applied integrals

1. ## Help with applied integrals

Hello all, while I'm just getting the hang of taking integrals, I still pretty much have no idea how to set them up in regards to real world senario problems such as (I need help with two problems in particular) these:

A thick rope holding a bucket of unused calendars, weighing 30lbs., hangs from the top of a 40-foot high building. The rope weighs 4lbs. per foot. Set up an integral for the work to raise the bucket from ground level up to 20 feet above the ground.

A 200-foot high dam is shaped by the symmetic function y = sqrt(2x +1)-1. The water level is at the top of the dam. Set up an integral that gives the total water pressure against the dam. Water weighs 62.4lbs per cubic foot.

I only need to setup the integral formula. Also, I haven't taken physics - the professor stated that while these problems require some physics, its nothing extensive. If possible can someone state the necessary steps I should take to tackle problems like these and briefly demonstrate it on one? Thanks.

2. ...Well I think got the function for the first problem:

The integral from 0 to 20 of : 4(40 - X) + 30.

The integral's interval corresponds to the 20 foot distance the problem is asking for, and 4(40 - X) + 30 is the ropes weight (4lbs) multiplied by the length left (40 - X) plus the weight of the bucket (30lbs). Does this look right to anyone? thanks

3. You want your equation for the dam problem in terms of y.

$\displaystyle x=\frac{(y+1)^{2}-1}{2}$