6. Set up and evaluate the double integral se siguin Z= xy, z>0, and 3x <...
for b.
y= sin(x^2-3x+1)
og t par Set up, but do not evaluate, the integral required to compute the arc length of the curve cotr. y= 217from 0<x< /2. mense metied to compute Set up, but do not evaluate, the integral required to compute the surface area of the solid obtained by rotating the curve y=sin(x2 3x + 1), 0<x< 1 about the z-axis.
3. (2 pts) Set up a triple integral that calculates the mass of an object that occupies the region r >0, y > 0,=> 0 and 3/3+y/6+2/9 <18, where the density of the object is given by 02, y, z) = 6 - 2. Do not evaluate the integral
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
2.) Let Z the set of integers and two binary operations on it: Z23(x,y) → xTy = xy + 3x +3y +6 e Z i) Show (Z,L,T)is an integral domain ii) Find the set of units U(Z)
2.) Let Z the set of integers and two binary operations on it: Z23(x,y) → xTy = xy + 3x +3y +6 e Z i) Show (Z,L,T)is an integral domain ii) Find the set of units U(Z)
4 Set up and evaluate a double integral to find the volume of the solid bounded by the graph of the equations y # 4-x2.z # 4-r2, first octant
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = (x2, yz, zº) through the open-ended circular cylinder of radius 5 and height 4 with its base on the xy-plane and centered about the positive z-axis, oriented away from the z-axis. If necessary, enter 6 as theta. Flux = -MIT" dz de A= BE C= D= (b) Evaluate the integral. Flux = S]
set up iterated integrals for both orders of integration. then
evaluate the double integral using the easier order and explain why
it's easier.
D y dA, D is bounded by y = x - 2,
x=y2 (the D next to the double integral
should be under the integral. I don't know how to put it in the
right spot.
Evaluate the given double integral by changing it to an iterated integral. xy dA; S is the triangular region with vertices (0,0), (10,0), and (0,7) O 35 12 0 1225 6 245 12 175 6
2. Set up and evaluate the volume integral for the region whose base D lies in the first quadrant in the xy plane and whose top is bounded by x + y + z = 4. 3. Find the volume that is enclosed by both the cone z = x2 + y2 and the sphere x2 + y2 + z = 2
Using both type I and type II region evaluate double integral SSR xy dĀ, with the region R enclosed by x = y2, y + x = 6 and y = 0.