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.

- anonymous

- schrodinger

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- anonymous

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

- anonymous

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

- bahrom7893

why 0 to 3?

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## More answers

- anonymous

oh, because 300 m deep along dirt road

- bahrom7893

Oh okay

- anonymous

do you think this needs a double integral?

- bahrom7893

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?

- anonymous

dont know how to set up double integral for this one

- anonymous

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

- anonymous

since total area = integral y(x)*dx

- anonymous

so i look at integration as summing the infinitely thin rectangles

- bahrom7893

what is the answer?

- anonymous

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

- anonymous

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

- anonymous

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

- bahrom7893

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

- bahrom7893

and math is hard, im regretting my math majorin decision

- anonymous

oh
are you undergrad?

- bahrom7893

yeah, im a freshman

- anonymous

what country?

- bahrom7893

US

- anonymous

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

- anonymous

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

- bahrom7893

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

- anonymous

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

- anonymous

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

- bahrom7893

yeah

- bahrom7893

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

- anonymous

oh there is units issue

- bahrom7893

100 meters?

- anonymous

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

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