A contour map is shown for a function
f
\displaystyle {f}
f
on the square
R
=
[
0
,
4
]
×
[
0
,
4
]
\displaystyle {R}={\left[{0},{4}\right]}\times{\left[{0},{4}\right]}
R
=
[
0
,
4
]
×
[
0
,
4
]
2
4
2
4
19
10
5
5
10
10
19
19
[Graphs generated by this script: initPicture(-.5,4.5,-.5,4.5);axes(2,2,1,1,1);circle([2,0],.707);circle([2,0],1.581);circle([4,3],.707);circle([0,3],.707);line([-1,0],[4,5]);line([0,5],[5,0]);ellipse([5,3],2,1.5);ellipse([-1,3],2,1.5);fontstroke='blue';fontfill='blue';text([2,.5],'19');text([2,1.8],'10');text([1.6,3.6],'5');text([2.4,3.6],'5');text([2.8,3],'10');text([1.2,3],'10');text([3.5,3],'19');text([.5,3],'19');]
Use the Midpoint Rule with
m
=
n
=
4
\displaystyle {m}={n}={4}
m
=
n
=
4
to estimate the value for
∫
∫
R
f
(
x
,
y
)
d
A
\displaystyle \int\int_{{R}}{f{{\left({x},{y}\right)}}}{d}{A}
∫
∫
R
f
(
x
,
y
)
d
A
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Question 6
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\displaystyle
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity