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bixtya [17]
3 years ago
15

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.
Mathematics
1 answer:
kherson [118]3 years ago
7 0

Answer:

The Area of the Enclosed Region Is 64/3.

Step-by-step explanation:

As Given in Question

We have, Curve 4x+Y^{2}=12

& X=Y

Solution.

4Y+Y^{2}=12   (X=Y)

Y^{2}+4Y-12=0

Y^{2}+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

by Solving This Equation we get Area of Region = 64/3 .    

this equation Solution & Curve Diagram please see In Attachment .  

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