Question

Area of a roof over an ellipse Find the area of the surface S that lies
in the plane z = 12 - 4x - 3y directly above the region R bounded by the ellipse x2/4 + y2 = 1.

z = 12 – 4x – 3y
S is directly above R.
12
--
R is bounded by the ellipse
+ y? = 1.
Area of S = V26 x area of R.
Figure 17.53
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Applications of Integration

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Transcribed Image Text

z = 12 – 4x – 3y S is directly above R. 12 -- R is bounded by the ellipse + y? = 1. Area of S = V26 x area of R. Figure 17.53