Question

just checking over solution for question:
A tract of land bordered by a highway along the y-axis, a dirt road along the x-axis, and a river whose path is given by the equation y=4-0.2x^2, where x and y are in hindreds of meters.

The tract is 300m deep along the dirt road The value of the land is constant in any strip parallel to the highway and increases as you move way from the highway, with the value given by v=1000+50x dollars per 10,000 m^2 at the sample point (x,y). Find dW, the worth of a strip. Write an integral that equals the worth of the entire tract.

Answer 1

here is my solution. we have integral dw, where dw is a strip of the "worth" of the land.
The dw is like Area(x)*value(x) at x as you go along , but Area(x) is y(x)*dx

Answer 2

so integral (4 - .2x^2) ( 1000 + 50x) dx from 0 to 3

Answer 3

why 0 to 3?

Answer 4

oh, because 300 m deep along dirt road

Answer 5

Oh okay

Answer 6

do you think this needs a double integral?

Answer 7

i honestly have no idea, did you try both ways? One with a double integral one with a regular one and solve them on the calculator and check the answer?

Answer 8

dont know how to set up double integral for this one

Answer 9

if the value was constant, we would have k integral y(x)* dx , where y(x)*dx is a strip of area (or a infinitely thin rectangle). but its changing so we have to put it inside the integral

Answer 10

since total area = integral y(x)*dx

Answer 11

so i look at integration as summing the infinitely thin rectangles

Answer 12

what is the answer?

Answer 13

oh i dont really care about the answer. i just want to set it up correctly , lol

Answer 14

math people just prove a solution exists, they leave the calculations for another day, i suppose

Answer 15

well the ancient greeks let the slaves approximate. but i think archimedes was the first to sit down and approximate pi to many digits

Answer 16

i mean if u knew the answer, we could see if ur setup was correct. I tried it on the calculator and got 0.009561, etc

Answer 17

and math is hard, im regretting my math majorin decision

Answer 18

oh
are you undergrad?

Answer 19

yeah, im a freshman

Answer 20

what country?

Answer 21

US

Answer 22

youre doing great if youre freshman, and solved that integral problem
the e^x

Answer 23

of course math takes effort . but i hit a wall in math personally. in the advanced math stuff,

Answer 24

i took calc 1 and 2 in hs, it was okay, calc 3 knocked me down in college

Answer 25

you can do math for engineering , and that will allow you avoid the advanced formal stuff like topology, for example

Answer 26

calc 3 is hard. lol. you have to go over it more than once. i have my own gaps in knowledge. have you tried khanacademy.org

Answer 27

yeah

Answer 28

okay just finished half of my own hw, sorry gtg ttyl, bye

Answer 29

oh there is units issue

Answer 30

100 meters?

Answer 31

no its fine
well the y dx is 100 meters * 100 meters, so 10000 m^2, but the value is per 10,000 m^2 , so they cancel.
i got 10897.5 as the answer