Question

Set
up BUT DO NOT SOLVE an integral or integrals that give the area
between the two loops of the curve r=3+6sin(θ)

plz answer ASAP

Answer #2

Please appreciate my work.

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answered by: anonymous

Set up the integral that would give the area that is bounded
between these functions.
y =x/5
x = y2 − 3y

Set up, but do not evaluate or simplify, the definite
integral(s) which could be used to find the area of the region made
up of points inside of both the circle r = cos(θ) and the rose r =
sin(2θ)

a) Set up the integral used to find the area contained in one
petal of r= 3cos(5theta)
b) Determine the exact length of the arc r= theta^2 on the
interval theta= 0 to theta=2pi
c) Determine the area contained inside the lemniscate r^2=
sin(2theta)
d) Determine the slope of the tangent line to the curve r= theta
at theta= pi/3

Set up, but do not solve, the triple integral for determining
the mass of the sphere ? = 10 sin? sin ? with a density of ?(?,?,
?) = ?.

Set up integrals for both orders of integration. Use the more
convenient order to evaluate the integral over the plane region
R.
R
4xy dA
R: rectangle with vertices (0, 0), (0, 3), (2, 3), (2, 0)

Set up the definite integral(s) that represents the area between
the curves y = x2 - 6 and y = x

3. Set up two double integrals giving the area enclosed by the
curves y = x^2 and y = x + 2 and evaluate one of them.

Set up iterated integrals for both orders of integration. Then
evaluate the double integral using the easier order.
y dA, D is bounded by y = x
− 20; x = y2
D

Instructions: For each region described, set up, BUT DO NOT
EVALUATE, a single definite integral that represents the exact area
of the region. You must give explicit functions as your integrands,
and specify limits in each case. You do not need to evaluate the
resulting integral.
1. The region enclosed by the lines y=x, y=2x and y=4.
2. The region enclosed by the curve y=x^2 and the line
y=5x+6.
3. The portion of the region inside the circle x^2+y^2 =4...

Set up, but do not evaluate, an integral of f(x,y,z) = 20−z over
the solid region deﬁned by
x^2 +y^2 +z^2 ≤ 25 and z ≥ 3. Write the iterated integral(s) to
evaluate this in a coordinate system of your choosing, including
the integrand, order of integration, and bounds on the
integrals.

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