Solutions
MATH 234-0 S67 Spring 2014
Homework #9
14.M.4 Evaluate the integral
of integration.
84
0
x2/3
x cos y4 dy dx by rst reversing the order
Indeed, this integral cannot be done in the order y then x. So, draw the region:
y
4
4
3
x
0
x
y3 2
2
1
0
0
2
MA 234-0 (Bostwick SP14) Homework #2 Solutions
Section 14.3
14.3.3 Use double integration to nd the area of the region bounded by y =
x2 and y = 2x + 3.
The x limits are given by the intersections of the curves:
x2 = y = 2x + 3
=
=
=
x2 2x 3 = 0
( x 3) (
MA 234-0 (Lec. 67) Homework #8 Solutions - Spring
2014
Section 15.6
15.6.2
Verify the divergence theorem for F = |r | r and S the spherical surface given
by x2 + y2 + z2 = 9.
The vectors normal to the surface point radially out from the origin, so n =
and
Solutions
MATH 234-0 Section 67, Spring 2014
Homework #7
15.1.21 Calculate the divergence and curl of the vector eld F ( x, y, z) =
y2 + z2 + x2 + z2 + x2 + y2 k.
i
j
F and
Formally, this is
F. So, using ordered-triplet notation:
, ,
x y z
F =
y2 + z2
MA 234-0 (Lec. 67) Homework #5 Solutions
Section 15.1
15.1.3
Sketch typical vectors in the vector eld F ( x, y) = xi y j
1.0
y
0.5
0.0
0.5
1.0
1.0
0.5
0.0
x
0.5
1.0
15.1.5
Sketch typical vectors in the vector eld F ( x, y) =
x 2 + y2 x i + y j
The vectors
Miscellaneous Integrals (Answers)
Instructions: For each of the following, you should be able to perform each of the integrations and
dierentiate the result to get back to the original integrand without any errors.
1.
1
dx = 2 tan1 ( x) + C
(1 + x) x
2.
MA 234-0 (Lec. 67,77) Homework #1 Solutions
Section 14.1
14.1.12
32
Evaluate the iterated integral 0 0 x2 y dx dy.
Compute the inner, x, integral rst, holding y constant:
3 2
x2 y dx dy
0
=
=
0
3
0
0
3
0
=
2
3
0
x2 y dx
1 3
x y
3
2
x =0
!
!
dy
dy
8
y dy
3
Miscellaneous Integrals
Instructions: For each of the following, you should be able to perform each of the integrations and
dierentiate the result to get back to the original integrand without any errors.
1.
1
dx
(1 + x) x
20.
cos 2x
dx
cos x
39.
ex
2.
s