SECTION 1: Antiderivatives, Integrals and Applications
1. Evaluate each integral.
a) 6
4
xdx
x
+
∫ b)
21
2
4
1
x
xe dx
x
+
+
∫
c) 3ln(2 )
x
xdx
∫ d)
()
2
2
04
xdx
x+
∫
2. Evaluate the improper integral.
a) 2
2
04
xdx
x−
∫ b)
1
0
3ln4
x
dx
x
∫
3. Evaluate the integral by reversing the order of integration.
2
13
3
0
x
yedxdy
∫∫
4. Find the area under the curve drawn.
π
6
1
2
x
+ 2
y
= 2
x
y
5. Find the volume of the plane ounded by the
first octant. ( )
63 6zx=− −
y
b
0, 0xy≥≥
6. Find the volume under the surface cos( )zx y
=
that lies above
the region in the xy plane that is bounded by
2,0 1
y
x y and x== =. The three dimensional graph is not
shown, due to lack of appropriate software.
