Integral Word Problem EXACT PROBLEM Incluced

[niravana21]

Homework Statement

Here is the problem:

The Attempt at a Solution

I can see that as x increases, the deeper the water gets, but I can't figure out my limits of integration.

If somecan just give me the limits, I think I would be all set.

 

[jhae2.718]

The depth of the pool is modeled by D(x)=1+x²/175.

According to the problem, the pool is 25 meters long. This is from the shallow end to the deep end.

Knowing that your interval should be as long as the length of the pool, what do you think you should use?

 

[Dunkle]

The equation for depth involves x, the distance from the shallow end. The pool is 25 meters long. Given this information, what do you think the limits should be?

Edit: Whoops, a little late!

 

[niravana21]

0 to 25?

 

[jgens]

Yup.

 

[jhae2.718]

Correct. Generally, whenever you need to integrate something of a fixed length l, your interval should be from 0 to l. This includes when finding area, volume, time, etc, which if you haven't done yet you will. You'll always get your interval from the problem; sometimes you may have to solve for your limits of integration.

 

[niravana21]

thanks so much guys. Feel like an idiot.

Feels good to solve a problem.

thanks again. Will definitely post back again.