Evaluate the following integral ∫ ∫ R 4x + y (3x − y) ln(3x − y)...
Evaluate the following integral ∫ ∫ R 4x + y (3x − y) ln(3x − y)
dA where R is the region bounded by the graphs of y = 3x − e7,
y = 3x − e5, y = −4x + 8, and y = −4x + 5. Use the change
of variables u = 3x − y, v = 4x + y.
using / for integral
Evaluate the double integral //R cos( (y-x)/(y+x) )dA where R is
the trapezoidal region with vertices (1,0), (2,0), (0,2), and
(0,1)
1. Evaluate the double integral for the function
f(x,y) and the given region
R.
R is the rectangle defined by
-2 x 3 and
1 y e4
2. Evaluate the double integral
f(x, y) dA
R
for the function f(x, y) and the
region R.
f(x, y) =
y
x3 + 9
; R is bounded by the lines
x = 1, y = 0, and y = x.
3. Find the average value of the function
f(x,y) over the plane region
R....
consider the following equation,
max r = 4x + y + 6z
2x + y + 2z <= 10
x + 2y + z <= 9
x + 2z <= 6
x, y, z >= 0
The tableau corresponds with a step of the SIMPLEX method
applied to the previous problem
Basic
x
y
z
s1
s2
s3
bi
s1
1
1
0
1
0
-1
4
s2
1 / 2
2
0
0
1
-1 / 2
6
z...
Use the given transformation to evaluate the integral. (12x +
8y) dA R , where R is the parallelogram with vertices (−1, 3), (1,
−3), (2, −2), and (0, 4) ; x = 1/ 4 (u + v), y = 1/ 4 (v − 3u)