HOW DO YOU SEE IT? Consider the surface f ( x , y ) = x 2 + y 2 (see figure) and the surface area f that lies above each region R . Without integrating, order the surface areas from least to greatest. Explain. (a) R : rectangle with vertices ( 0 , 0 ) , ( 2 , 0 ) , ( 2 , 2 ) , ( 0 , 2 ) (b) R : triangle with vertices ( 0 , 0 ) , ( 2 , 0 ) , ( 2 , 2 ) (c) R = { ( x , y ) : x 2 + y 2 ≤ 4 , first quadrant only }
HOW DO YOU SEE IT? Consider the surface
f
(
x
,
y
)
=
x
2
+
y
2
(see figure) and the surface area
f
that lies above each region
R
. Without integrating, order the surface areas from least to greatest. Explain.
Vertical and Horizontal area of the plane region y=2x^2+1 and y=x^2+5
Surface integrals using an explicit description Evaluate the surface integral ∫∫S ƒ(x, y, z) dS using an explicit representation of the surface.
ƒ(x, y, z) = 25 - x2 - y2; S is the hemisphere centered at theorigin with radius 5, for z ≥ 0.
check_circleAnswered about 2 hours ago
PLANE AREAFind the area of the region bounded by given curves. Label each plane
x3-2x+2y-3=0 and 2x+3y+6=0
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