Question

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

Answer #1

please comment if you have any doubts will clarify

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

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

57.
a. Use polar coordinates to compute the (double integral (sub
R)?? x dA, R x2 + y2) where R is the region in the first quadrant
between the circles x2 + y2 = 1 and x2 + y2 = 2.
b. Set up but do not evaluate a double integral for the mass of
the lamina D={(x,y):1≤x≤3, 1≤y≤x3} with density function ρ(x, y) =
1 + x2 + y2.
c. Compute??? the (triple integral of ez/ydV), where E=
{(x,y,z):...

Evaluate the double integral of 5x3cos(y3)
dA where D is the region bounded by y=2, y=(1/4)x2, and
the y-axis.

evaluate the double integral x^2 y da, r is 9x^2+4y^2=36, use
x=2u and y=3r

Use the given transformation to evaluate the integral.
(x −
8y) dA,
R
where R is the triangular region with vertices (0, 0),
(7, 1), and (1, 7).
x = 7u +
v, y = u +
7v

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)

Use the given transformation to evaluate the integral.
6xy dA
R
, where R is the region in the first quadrant bounded
by the lines y =
1
2
x and y =
3
2
x and the hyperbolas xy =
1
2
and xy =
3
2
;
x = u/v, y = v

evaluate the double integral
D (xsiny) dA
D is bounded by y = 1, y=x, and x=2

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