Question

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

Answer #1

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

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 =
2
3
x and y =
3
2
x and the hyperbolas xy =
2
3
and xy =
3
2
;
x = u/v, y = v

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

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...

let R be the region bounded by the curves x = y^2 and x=2y-y^2.
sketch the region R and express the area R as an iterated integral.
(do not need to evaluate integral)

(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 a change of variables to evaluate Z Z R (y − x) dA, where R
is the region bounded by the lines y = 2x, y = 3x, y = x + 1, and y
= x + 2. Use the change of variables u = y x and v = y − x.

Use the given transformation to evaluate the integral. 6y2 dA, R
where R is the region bounded by the curves xy = 3, xy = 6, xy2 = 3
and xy2 = 6; u = xy, v = xy2

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

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

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 14 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 21 minutes ago

asked 25 minutes ago

asked 32 minutes ago

asked 34 minutes ago

asked 36 minutes ago

asked 59 minutes ago