Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating
rectangle and label its height and width.4x+y^2=12, x=yThen find the area S of the region.
1 answer:
Answer:
The Area of the Enclosed Region Is 64/3.
Step-by-step explanation:
As Given in Question
We have, Curve 4x+
=12
& X=Y
Solution.
4Y+
=12 (X=Y)
+4Y-12=0
+6Y-2Y-12=0
Y(Y+6)-2(Y+6)=0
(Y-2)*(Y+6)=0
Y=2 & -6 (X=Y)
Now at (2,2) & (-6,-6) both curves intersect each other.
The Area Of Enclosed Region is ![\int\limits^2_{-6} [(3-Y^{2}/4 )-Y] \, dy](https://tex.z-dn.net/?f=%5Cint%5Climits%5E2_%7B-6%7D%20%5B%283-Y%5E%7B2%7D%2F4%20%29-Y%5D%20%20%5C%2C%20dy)
by Solving This Equation we get Area of Region = 64/3 .
this equation Solution & Curve Diagram please see In Attachment .
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