MATH 251 – LECTURE 20 http://www.math.tamu.edu/~jensf/
This week: 13.9–10 webAssign: 13.8–10, due 3/21 11:55 p.m.
M W: Kevin
F: no lecture
After spring break: webAssign: nope
M: Review chapter 13
W: Midterm 2
Help Sessions: M W 5.30–8 p.m. in BLOC 161
Office Hours:
BLOC 641C
M 12:30–2:30 p.m.
W 2–3 p.m.
or by appointment.

Cylindrical coordinates
Exercise 1 .
Compute the triple integral
RRR
E e x
2
+ y
2 dV where E is the domain E = { x
2
+ y
2 ≤ 1 , 0 ≤ z ≤ 1 } .

Cylindrical coordinates
Cylindrical coordinates are polar coordinates in two variables, and rectangular coordinates in the third variable.


 x = r cos( θ ) y = r sin( θ ) z = z

Cylindrical coordinates
Exercise 2 .
Write the equation 7 z = 3 x
2
+ 3 y
2 in cylindrical coordinates.

Cylindrical coordinates
Exercise 3 .
Compute the volume of the domain E = { x
2
+ y
2 ≤ 1 , 0 ≤ z ≤ x
2 } .

Cylindrical coordinates
Exercise 3 .
Compute the volume of the domain E = { x
2
+ y
2 ≤ 1 , 0 ≤ z ≤ x
2 } .

Cylindrical coordinates
Exercise 4 .
Evaluate the integral
RRR x
2 dV , where E is the solid that lies within the cylinder x
2
E above the plane z = 0 and below the cone z 2 = 49 x 2 + 49 y 2 .
+ y
2
= 9,

Cylindrical coordinates
Exercise 4 .
Evaluate the integral
RRR x
2 dV , where E is the solid that lies within the cylinder x
2
E above the plane z = 0 and below the cone z 2 = 49 x 2 + 49 y 2 .
+ y
2
= 9,