[T] Consider the function f ( x , y ) = sin ( x 2 ) cos ( y 2 ) . where ( x. y ) ( x , y ) ∈ R = [ − 1 , 1 ] × [ − 1 , 1 ] . a. Use the midpoint rule with m = n = 2. 4,. ... 10 to estimate the double integral I = ∬ R sin ( x 2 ) cos ( y 2 ) d A . Round your answers to the nearest hundredths. b. For m = n = 2. find the average value of f over the region R. Round your answer to the nearest hundredths. c. Use a CAS to graph in the same coordinate system the solid whose volume is given by ∬ R sin ( x 2 ) cos ( y 2 ) d A and the plane z = f a v e
[T] Consider the function f ( x , y ) = sin ( x 2 ) cos ( y 2 ) . where ( x. y ) ( x , y ) ∈ R = [ − 1 , 1 ] × [ − 1 , 1 ] . a. Use the midpoint rule with m = n = 2. 4,. ... 10 to estimate the double integral I = ∬ R sin ( x 2 ) cos ( y 2 ) d A . Round your answers to the nearest hundredths. b. For m = n = 2. find the average value of f over the region R. Round your answer to the nearest hundredths. c. Use a CAS to graph in the same coordinate system the solid whose volume is given by ∬ R sin ( x 2 ) cos ( y 2 ) d A and the plane z = f a v e
[T] Consider the function
f
(
x
,
y
)
=
sin
(
x
2
)
cos
(
y
2
)
. where (x. y)
(
x
,
y
)
∈
R
=
[
−
1
,
1
]
×
[
−
1
,
1
]
.
a. Use the midpoint rule with m= n = 2. 4,. ... 10 to estimate the double integral
I
=
∬
R
sin
(
x
2
)
cos
(
y
2
)
d
A
. Round your answers to the nearest hundredths.
b. For m = n = 2. find the average value of f over the region R. Round your answer to the nearest hundredths.
c. Use a CAS to graph in the same coordinate system the solid whose volume is given by
∬
R
sin
(
x
2
)
cos
(
y
2
)
d
A
and the plane
z
=
f
a
v
e
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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Numerical Integration Introduction l Trapezoidal Rule Simpson's 1/3 Rule l Simpson's 3/8 l GATE 2021; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=zadUB3NwFtQ;License: Standard YouTube License, CC-BY