In the following exercises, estimate the volume of the solid under the surface z = f(x. y) and above the rectangular legion R by using a Riemann sum with m = n = 2 and the sample points to be the lower left corners of the subrectangles of the partition. 11. The solid lying under the surface z = 4 − y 2 and above the rectangular region R = [0. 2] × [0, 2] is illustrated in the following graph. Evaluate the double integral ∬ R f ( x , y ) d A . where f ( x , y ) = 4 − y 2 . by finding the volume of the corresponding solid.
In the following exercises, estimate the volume of the solid under the surface z = f(x. y) and above the rectangular legion R by using a Riemann sum with m = n = 2 and the sample points to be the lower left corners of the subrectangles of the partition. 11. The solid lying under the surface z = 4 − y 2 and above the rectangular region R = [0. 2] × [0, 2] is illustrated in the following graph. Evaluate the double integral ∬ R f ( x , y ) d A . where f ( x , y ) = 4 − y 2 . by finding the volume of the corresponding solid.
In the following exercises, estimate the volume of the solid under the surface z= f(x. y) and above the rectangular
legion R by using a Riemann sum with m = n = 2 and the sample points to be the lower left corners of the subrectangles of the partition.
11. The solid lying under the surface
z
=
4
−
y
2
and above the rectangular region R = [0. 2]
×
[0, 2] is illustrated in the following graph. Evaluate the double integral
∬
R
f
(
x
,
y
)
d
A
. where
f
(
x
,
y
)
=
4
−
y
2
. by finding the volume of the corresponding solid.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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