MA 126-E0 Summer 2006 Test 1
1. Evaluate R1
0(3x+ 1)e๎xdx.
2. Evaluate Z4
3
x๎9
x2+ 3x๎10dx:
3. Evaluate R1
0x2(1 + 2x3)5dx.
4. Suppose we want to approximate R5=2
2sin(x2)dx.
(a) Find a value of nso that the midpoint approximation using nsubdivisions
of the interval will be within 1=100 of the value of this integral.
(b) Write out the terms of the midpoint approximation for this value of n.
(Do not attempt to evaluate this sum).
5. Find the area bounded by the graphs of y= sin(x)and y= 1=2for
0๎x๎๎=2.
6. Determine whether the following integral converges ot diverges:
Z1
1
1
(3x+ 1)2dx:
If the integral converges, determine its value. If the integral diverges, it has no
numerical value.
7. Let Dbe the region bounded by the graphs of y=e2x,x=๎1and x= 2,
and the x๎axis. Find the volume of the solid that results if Dis rotated about
the x๎axis.
Each problem is worth 16 points. In Problem 4, (a) is worth 10 points, and
(b), 6points.
1