The discussion revolves around finding the value of c for the area enclosed by two parabolas, y = x² - c² and y = c² - x², to equal 110. Participants are exploring the mathematical reasoning and calculations involved in determining this value.
There is ongoing exploration of the calculations and methods used to find c, with some participants expressing uncertainty about their approaches. Guidance is offered regarding the integration setup and the interpretation of the curves involved. Multiple values are being considered, and participants are questioning the accuracy of their results.
Participants mention the need to express the result exactly, and there is a reference to a similar problem discussed by a professor, which adds to the complexity of the current problem. Some participants express confusion about whether their mathematical setup is correct.
intelli said:Find c>0 such that the area of the region enclosed by the parabolas y= x^2-c^2 and
y = c^2-x^2 is 110
what is value of c
i got 3.49 and it is wrong i don't understand how to do this problem any help would be greatly appreciated
berkeman said:How did you get 3.49? Show us your work please.
berkeman said:How did you get 3.49? Show us your work please.
Dick said:I get 3.45... as well. But that's not the same as 3.49. Maybe they want you to express it exactly using a cube root?
intelli said:no i tried that it doesn't work
Dick said:It looks fine to me.
berkeman said:I agree. Ask the prof, and please post the final answer back here. Thanks.
Dick said:I think he is figuring out which curve is on top of the region (y=c^2-x^2) and which is on the bottom (y=x^2-c^2) and then the x boundaries +c and -c. He think subtracts the lower curve y from the upper curve y and integrates over the whole region at once (rather than doing the first quadrant and multiplying by 4, like you did). But if you do his final integral, you get (8/3)*c^3. Just as you did.