Homework Statement
Evaluate the triple integral \int\int\int^{}_{E} xy dV where E is the tetrahedron (0,0,0),(3,0,0),(0,5,0),(0,0,6).
Is there a simple way to simplify the integration?
Homework Equations
The Attempt at a Solution
\frac{z}{6} + \frac{y}{5} + \frac{x}{3} = 1
z =...
Homework Statement
\int\int\int^{}_{B} ye^(-xy) dV where B is the box determined by 0 \leq x \leq 4, 0 \leq y \leq 1, 0 \leq z \leq 5.
Homework Equations
The Attempt at a Solution
\int^{4}_{0}\int^{1}_{0}\int^{5}_{0} ye^(-xy) dzdydx
Integrating the first time I get
zye-xy
Plugging in 5...
Homework Statement
Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x2 + y2 = 256 and x2 - 16x + y2 = 0.
Homework Equations
The Attempt at a Solution
Finding the intervals of integration for the polar coordinates...
Homework Statement
Suppose D is the parallelogram enclosed by the lines 2x-3y = 0, 2x-3y = 2, 3x-y = 0 and 3x-y = 1.
\int\int^{}_{D} [(2x-3y) e^(3x-y) dA
Homework Equations
The Attempt at a Solution
Set u to be equal to 2x-3y -> x = (u+3y)/2
Set v to be equal to 3x-y -> v = 3/2(u+3y)-y...
Homework Statement
Suppose D is the parallelogram in the xy-plane with vertices P(-1,5), Q(1,-5), R(5,-1), S(3,9)
\int\int ^{}_{D} (6x+12y) dA
HINT: Use transformation x = \frac{1}{6}(u+v) and y = \frac{1}{6} (-5u+v).
Homework Equations
The Attempt at a Solution
Calculating the Jacobian I...
Homework Statement
Evaluate the integral by reversing the order of integration.
\int^{3}_{0}\int^{9}_{y^2} y cos(x^2) dydx
Homework Equations
...?
The Attempt at a Solution
Drawing the picture out we get a sideways parabola.
From the picture I get the following intervals of integration...
Homework Statement
Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 9.
Homework Equations
. . . ?
The Attempt at a Solution
After drawing out the picture with z=0 I have a line going from 0,9 to 9,0 bounded by the x and y axis giving me a triangle...
Homework Statement
Evaluate the iterated integral I = \int^{1}_{0}\int^{1+y}_{1-y} (6y^2+ 10x) dxdy
Homework Equations
. . . ?
The Attempt at a Solution
Integrate with respect to x gives me the following equation.
\int^{1}_{0} 6xy^2 + 5x^2 dy
I plug in y+1 and y-1 into x and get the...
Homework Statement
Evaluate the double integral ∫∫D xy dA where D is the triangular region with vertices (0,0) (6,0) (0,1).
Homework Equations
The Attempt at a Solution
0 <= x <= -\frac{1}{6}x+1
0 <= x <= 6
the first integral would be the integral from 0 to -1/6x+1 of xy with...
Homework Statement
An implicit equation for the plane passing through the point (-2,5,-5) that is perpendicular to the line L(t) = <5+2t,3,4> is ...?
Homework Equations
a(x-x0) + b(y-y0) + c(z-z0) = 0
The Attempt at a Solution
So in order to find the equation of the plane I would...
Homework Statement
Find an equation of a plane containing the three points (1, -1, 0), (5, 4, 1), (5, 5, 3) in which the coefficient of x is 9. What does it mean when it says the coefficient of x is 9?
Homework Equations
a(x-x0) + b(y-y0) + c(z-z0) = 0
The Attempt at a Solution...
Homework Statement
Find the distance from the point (2, 4, 4) to the line x = 0, y = 4 + 3t, z = 4 + 2t.
Homework Equations
The cross product and the dot product and d = |n * b|/|n|
The Attempt at a Solution
So the distance from the point to the line is the line directly...
Homework Statement
A spherical source radiates sound uniformly in all directions. At a distance of 9 m, the sound intensity level is 100 dB. What power is radiated by this source?
Just a simple answer check to see if my answer is reasonable.
Homework Equations
\beta = 10 db log (I/I0)...
Homework Statement
A raft is made of 11 logs lashed together. Each is 35 cm in diameter and has a length of 5.6 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 70 kg? Do not neglect the weight of the logs. Assume the...
Homework Statement
So the original problem goes as the following.
A uniform ladder of mass (m) and length (L) leans against a frictionless wall, see figure. If the coefficient of static friction between the ladder and the ground is 0.41, what is the minimum angle (q) between the ladder and...
Homework Statement
Let y be the the solution of the initial value problem. The maximum value of y is?
y" + y = -sin(2x)
y(0) = 0
y'(0) = 0
Homework Equations
N/A
The Attempt at a Solution
Factor out original equation to find general equation.
r2 + 1 = 0
r = 0 + i; 0- i
Thus...
Homework Statement
y"' -9y" +18y" = 30ex. Does not matter what the initial conditions are for my question.
Homework Equations
N/A
The Attempt at a Solution
So I factored out the equation and got:
r*(r2 - 9r + 18)
Which gives roots r = 0, r = 3, r = 6.
Which gives me the general...
Homework Statement
y4 - 6y3 + 9y2
y(0) = 19; y'(0) = 16; y"(0) = 9; y"'(0) = 0
Homework Equations
N/A
The Attempt at a Solution
Factored out the equation and obtained the following roots.
r2(r2-3) = 0 which gives r = 0 and r =3.
Using those roots, I make the following general...