Question

Evaluate the double integral for the function

* f*(

and the given region *R*.

* f*(

*R* is the rectangle defined by

5 ≤ * x* ≤ 6

and

2 ≤ * y* ≤ 4

Answer #1

Evaluate the double integral for the function
f(x,
y)
and the given region R.
f(x, y) =
5y + 4x;
R is the rectangle defined by
5 ≤ x ≤ 6
and
1 ≤ y ≤ 3

evaluate the double integral where f(x,y) = 6x^3*y - 4y^2 and D
is the region bounded by the curve y = -x^2 and the line x + y =
-2

2. Evaluate the double integral Z Z R e ^(x^ 2+y ^2) dA where R
is the semicircular region bounded by x ≥ 0 and x^2 + y^2 ≤ 4.
3. Find the volume of the region that is bounded above by the
sphere x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 +
y^2 .
4. Evaluate the integral Z Z R (12x^ 2 )(y^3) dA, where R is the
triangle with vertices...

Use the given transformation to evaluate the double integral of
(x-6y) dA, where R is the triangular region with vertices
(0, 0), (5, 1), and (1, 5).
x = 5u +
v, y = u +
5v

A table of values is given for a function f(x, y) defined on R =
[1, 3] × [0, 4].
0
1
2
3
4
1.0
2
0
-3
-6
-5
1.5
3
1
-4
-5
-6
2.0
4
3
0
-5
-8
2.5
5
4
3
-1
-4
3.0
7
8
6
3
0
Estimate f(x, y) dA R using the Midpoint Rule with m = n = 2 and
estimate the double integral with m = n =...

Use the given transformation to evaluate the double integral.
(12x + 12y) dA R , where R is the parallelogram with vertices (−3,
6), (3, −6), (4, −5), and (−2, 7) ; x = 1/ 3 *(u + v), y = 1 /3* (v
− 2u)

using the change of variable x =u/v, y=v evaluate "double
integral(x^2+2y^2)dxdy: R is the region in the first quadrant
bounded by the graphs of xy=1, xy=2, y=x, y=2x

Using both type 1 and type 2 region evaluate double
integral §§R (2x - 1)dA with R enclosed by y + x - 1=0 , y - x = 1
and y = 2

(9)
(a)Find the double integral of the function f (x, y) = x + 2y
over the region in the plane bounded by the lines x = 0, y = x, and
y = 3 − 2x.
(b)Find the maximum and minimum values of 2x − 6y + 5 subject to
the constraint x^2 + 3(y^2) = 1.
(c)Consider the function f(x,y) = x^2 + xy. Find the directional
derivative of f at the point (−1, 3) in the direction...

Use the given transformation to evaluate the integral.
3x2dA,
R
where R is the region bounded by the ellipse
25x2 +
4y2 = 100;
x = 2u,
y = 5v

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