Math 1360
Exam 1 Review (Chapter 6-7.5)
Name___________________________________
1)
a)
Evaluate each of the following:
x
 e dx (Hint: Start with a u- substitution for the square root of x.)
 /4
b)
 sec
0
4
x tan 4 xdx
x 1
c)
 x( x  2)
d)

2
dx
25  x 2
dx
2) How many midpoint rectangles would you have to use in estimating the area under f(x)=2x
between x=0 and x=2 to get your answer accurate within 0.1? Hint: The derivative of bx is
(lnb)bx.(Your answer will look messy- that’s OK.)
3) Evaluate the following integrals:

1
a)  2 dx
1 x
1
b)
8
 x dx
0
4)
Set up, but do not evaluate, an integral to find the following:
a) The area of the region in the first quadrant bounded by y=tanx, y=1 and the y-axis.
b) The volume that results when the region bounded by y=x and y=x2 is rotated about the line
x=4.
c) The length of the curve that encloses the region bounded by y=x and y=x2.
d) The volume of the solid generated when the region bounded by y=sinx and y=cosx between
x=0 and x=π/4 is rotated about the y-axis.
e) The volume of the solid generated when the region in the first quadrant that is bounded by
x=y2, the y-axis and y=4 is rotated about y=5.
f) The volume that results when the region bounded by y= -x2+4 in the first quadrant is rotated
about the x-axis.
g) The surface area of the solid bounded by y=sinx, x=0, x=π/2 and the x-axis is rotated about the
x-axis.