Question

Consider the integral ∫∫R(x^2+sin(y))dA where R is the region bounded by the curves x=y^2, x=4, and y=0. Setup up this integral.

Answer #1

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...

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.

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)

Consider the region in the xy-plane bounded by the curves y =
3√x, x = 4 and y = 0.
(a) Draw this region in the plane.
(b) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the x-axis using the cross-section method.
(c) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the y-axis using the shell method.
(d) Set up the integral...

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

Sketch the region bounded by the given curves. y = 3 sin x, y =
ex, x = 0, x = π/2 Find the area of the region.

Evaluate ∫∫R(6xy+4)dA, ∫ ∫ R ( 6 x y + 4 ) d A , where R R is
the region bounded by y=x2 y = x 2 and y=x+2 y = x + 2 . (Round
your answer to 2 decimal places)

Let R be the region bounded by the curves y = x, y = x+ 2, x =
0, and x = 4. Find the volume of the solid generated when R is
revolved about the x-axis. In addition, include a carefully labeled
sketch as well as a typical approximating disk/washer.

Consider the plane region R bounded by the curve y = x − x 2 and
the x-axis. Set up, but do not evaluate, an integral to find the
volume of the solid generated by rotating R about the line x =
−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 =
2
3
x and y =
3
2
x and the hyperbolas xy =
2
3
and xy =
3
2
;
x = u/v, y = v

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