MATH 251 – LECTURE 33
JENS FORSGÅRD
http://www.math.tamu.edu/~jensf/
This week: Review
Friday:
webAssign: 14.7, due 4/25 11:55 p.m.
Midterm 3: 14.1–7
Next week: 14.8–9
webAssign: 14.8–9, opens 4/25 12 a.m.
Help Sessions:
Sun–Thu 6–8 p.m. in BLOC 149
Office Hours:
BLOC 641C
M 12:30–2:30 p.m.
W 2–3 p.m.
or by appointment.
Curve integrals
Z
Z
f ds
C
Z
F · dr.
f dx
C
C
Curve integrals
Z
F · dr.
C
Review
7. Let C be the unit circle, oriented counterclockwise. Compute
R
C
F · dr where
F = hxy − cos(sin(x)), x2 + ecos(y)i.
Review
17. Let C be the curve from (0, 0) to (5, 0) pictured below. Compute the curve integral
F (x, y) = hy, x + y + ey i.
R
C
F · dr, where
Review
8. Use curve integrals to compute the area between the x-axis and the graph y = sin(x), when 0 ≤ x ≤ π.
Review
12. Parametrize the cylindric surface given by x2 + y 2 = 4 and 0 ≤ z ≤ 2 − x.
Review
13. Parametrize the part of the cone given by x2 + y 2 = z 2 which is contained in the intersection of the solid
cylinder x2 + y 2 ≤ 2 and the half-plane z ≥ 0.
Surface integrals
Exercise 1. Compute the integral
0 ≤ u ≤ 1 and 0 ≤ v ≤ 1.
RR
S
x dS, where S is the surface parametrized by r(u, v) = hu, v, u2i for
Surface integrals
Exercise 2. Compute the integral
outwards, and F = hx, y, zi.
RR
S
F · dS where S is the cylinder x2 + y 2 = 1 for 0 ≤ z ≤ 1, with n pointing