Calculus integration application question

[Emmaa]

Hello, in this question my main concern is to find the integration bounds The concentration of pesticide at a particular point on a strip of land depends upon how close that point is to a nearby river. Land closer to the river has a greater amount of water run off passing over it towards the river, resulting in a lower pesticide concentration. At a point which is of distance x km from the river, the amount of the pesticide concentration at that point is 300/square root(400-x^2)
parts per million. The strip of land in question starts at the rivers edge and ends 10km away.


(a) Compute the average amount of pesticide over the strip of land.
(b) Can this model be used to examine the pesticide con- centration up to 20 km away from the river? Explain

 

[MarkFL]

What are the smallest and largest values of \(\displaystyle x\) which pertain to part (a)?

 

[DrPhil]

Hello, in this question my main concern is to find the integration bounds The concentration of pesticide at a particular point on a strip of land depends upon how close that point is to a nearby river. Land closer to the river has a greater amount of water run off passing over it towards the river, resulting in a lower pesticide concentration. At a point which is of distance x km from the river, the amount of the pesticide concentration at that point is 300/square root(400-x^2)
parts per million. The strip of land in question starts at the rivers edge and ends 10km away.


(a) Compute the average amount of pesticide over the strip of land.
(b) Can this model be used to examine the pesticide con- centration up to 20 km away from the river? Explain

To find the average over the strip of land defined to be \(\displaystyle 0 \le x \le 10\mathrm{km}\), your integrals will have to be from from \(\displaystyle 0\) to \(\displaystyle 10\mathrm{km}\). Supposedly the model function is adequate over that domain, but not necessarily accurate at larger \(\displaystyle x\). What happens if \(\displaystyle x \to 20\mathrm{km}\)?