1what is e to the power of ln x?
x
2how do you change the order of integration?
solve for x/y in terms of the other variable based off of limits
4what does x = in polar coords?
rcos(theta)
5what does y = in polar coords?
rsin(theta)
7when converting x^2+y^2 to r in the limits of R, what do you do to convert the limits in terms of r?
square root them
8what is the set up of a double integral in polar coords? dA=?
integralthet)integral(r) (solve for z equation)*r dr d(thet)
9when using symmetry to find the inside how do you set it up?
multiply 2 * greatest r value of the inside, (0<=thet<=end of the inside's theta) (0<=r<=r equation) r*dr*dthet
10when rewriting the order of an integral, what order do you solve for?
based off of the original equation's limit's, solve for the new limits in order of new dA, when solving, make sure to refer back to the original equations limits
11when solving a complicated integral what should you do?
change the order of integration by setting the respective variables to their limits and solving for one another, usually change the order based on the missing variable in the equation
12when making a triple integral what should you do?
solve for the limits given based off of one another and integrate in order of least resistance
13what is the set up of a cylindrical coordinate integral
Int(theta,r,z) (f(x,y,z) in terms of r)*r dzdrd(thet)
14what is integration by parts
select a u and a dv, then integrate v and solve for du
15what do you do when z= x+y (not z=x^2+y^2)
convert to polar coords( =rcos(thet)+rsin(thet))
16how do you set up spherical coordinate integration?
int(thet,φ(phi),p^2sin(phi)d(p)d(phi)d(thet)
17what does p^2=?
x^2+y^2+z^2
18when finding center of mass with radius r around the z axis, what is the center of mass for x and y?
0 and 0