Asked by Michael
Find the area of the region enclosed by the given curves:
4x+y^2=9, x=2y
4x+y^2=9, x=2y
Answers
Answered by
Steve
First, find where they intersect.
4x+y^2=9, x=2y
4(2y) + y^2 = 9
y^2 + 8y - 9 = 0
(y+9)(y-1) = 0
So, it might be easier to integrate in the y-direction:
∫[-9,1] (y^2-9)/4 - 2y dy
∫[-9,1] y^2/4 - 2y - 9/4 dy
y^3/12 - y^2 - 9/4 y [-9,1]
(-729/12 - 81 + 81/4) - (1/12 - 1 - 9/4)
355/3
4x+y^2=9, x=2y
4(2y) + y^2 = 9
y^2 + 8y - 9 = 0
(y+9)(y-1) = 0
So, it might be easier to integrate in the y-direction:
∫[-9,1] (y^2-9)/4 - 2y dy
∫[-9,1] y^2/4 - 2y - 9/4 dy
y^3/12 - y^2 - 9/4 y [-9,1]
(-729/12 - 81 + 81/4) - (1/12 - 1 - 9/4)
355/3
Answered by
Michael
Unfortunately, that answer is not right...
This is the last problem on my homework and I've been stuck on it for about an hour. Its very frustrating
This is the last problem on my homework and I've been stuck on it for about an hour. Its very frustrating
Answered by
Steve
How about 125/3 ?
If you had read my posting carefully (as I did not) you'd have noticed that it should have been
(9-y^2)/4
If you had read my posting carefully (as I did not) you'd have noticed that it should have been
(9-y^2)/4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.