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.
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
so integral (4 - .2x^2) ( 1000 + 50x) dx from 0 to 3
why 0 to 3?
oh, because 300 m deep along dirt road
do you think this needs a double integral?
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?
dont know how to set up double integral for this one
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
since total area = integral y(x)*dx
so i look at integration as summing the infinitely thin rectangles
what is the answer?
oh i dont really care about the answer. i just want to set it up correctly , lol
math people just prove a solution exists, they leave the calculations for another day, i suppose
well the ancient greeks let the slaves approximate. but i think archimedes was the first to sit down and approximate pi to many digits
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
and math is hard, im regretting my math majorin decision
oh are you undergrad?
yeah, im a freshman
youre doing great if youre freshman, and solved that integral problem the e^x
of course math takes effort . but i hit a wall in math personally. in the advanced math stuff,
i took calc 1 and 2 in hs, it was okay, calc 3 knocked me down in college
you can do math for engineering , and that will allow you avoid the advanced formal stuff like topology, for example
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
okay just finished half of my own hw, sorry gtg ttyl, bye
oh there is units issue
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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