Question

A forest is in the shape of a rectangle 5 miles long and 3 miles wide. The density of trees at a distance of x miles from the 5-mile side is given by p(x) trees per square mile. How do you express the number of trees in the forest?

Answer 1

taco

Answer 2

:( Please help! I have absolutely no idea how to do this and it was never covered in class.

Answer 3

this isn't a calculus question.

Answer 4

oh, maybe it is

Answer 5

See, that's what I told my teacher. Apparently it is somehow math and not magic.

Answer 6

first off, we need to decide. will this expression take integral or derivative form? check the title of the unit if you don't know :P

Answer 7

It's the midterm. I could be either. I thought it would be integral but I'm not sure.

Answer 8

I'm assuming you mean the midterm review, or I'm at least going to *pretend* for the time being for purposes of the code of conduct.

Answer 9

Yes I don't get midterms in almost ten pm

Answer 10

and yes, you are correct, this problem will result in an integral expression.

Answer 11

so, do you think this problem will be an indefinite integral or a definite integral?

Answer 12

I would think definite. Won't it have to stay within the rectangle?

Answer 13

Yes. Although you do not have an explicit number like 5, you would expect some kind of number and not an expression plus an arbitrary number C.

Answer 14

that being said, we can now think about what to do.

Answer 15

uhh

Answer 16

so would you integrate p(x)dx from three to five? I'm sorry, I'm so confused

Answer 17

ok. the idea of an integral is we add up a bunch of small rectangular increments (heavily simplifing and making somewhat flawed but reasonable assumptions)

right now, the main issue with the problem you are given is that you are not able to just take 3*5*p(x) and call it a day. Why not? because p(x) changes depending on something. Read over hte problem again. what does p(x) change depending on?

Answer 18

the distance of x miles

Answer 19

x miles? x miles in the 3 mile length direction or the five mile length direction?

Answer 20

so p(x) changes based on the density of the trees

Answer 21

no. p(x) IS the density of the trees.

Answer 22

density defined here as number of trees per square mile.

Answer 23

So then what does p(x) depend on?

Answer 24

the problem states it. "The density of trees at a distance of x miles from the 5-mile side is given by p(x) trees per square mile."