Study Guide for the 3rd Exam MTH241
Exam Date: 18th November 2011.
Exam Covers Sections 15
.
1

15
.
9
You must know the followings
1. Calculate double integrals.
2. Finding the volumes by using double integrations.
3. Changing the order of integrals.
4. Evaluating the integrals by changing to polar coordinates.
5. Evaluate surface integrals.
6. Evaluate triple integrals.
7. Finding volumes by triple integrations.
8. Finding triple integrations by changing to cylindrical and spherical coordinates.
Sample problems
These problems are not the exact problems but by solving these you can understand the hardness
of the original problems. Do the
homework problems and the problems which I discussed
in class
.
1. Evaluate
R R R
E
e
√
x
2
+
y
2
+
z
2
dV
by using the spherical coordinates. Where
E
is enclosed by the
sphere
x
2
+
y
2
+
z
2
= 9 in the ﬁrst octant.
2. Evaluate
R R R
T
xdV
by using the cylindrical coordinates. Where
T
is enclosed by the planes
z
= 0 and
z
=
x
+
y
+ 5 and by the cylinders
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 Fall '08
 RAMACHANDRAN
 Integrals

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