MTH 151
Quiz 7
Fall 2011
Show all work in a neat and organized fashion.
Clearly indicate your answers.
20 points possible.
1. (6 pts.) Take home problem. Find ∫46 x2 dx the "long way."
2. (6 pts.) Oil leaked from a tank at a rate of r(t) liters per hour. The
rate decraeased as time passed. Values of the rate at three-hour time intervals are shown
in the table.
t (hr)
0
3
6
9
12
15
r(t) (L/hr)
10.7
9.6
8.8
8.2
7.7
7.3
(a) Use a Riemann sum with right endpoints and five subintervals to estimate ∫015 r(t) dt, the total amount
of oil leaked out.
(b) Is your estimate greater or less than the true value?
3. (3 pts.) Determine a definite integral that is equal to the given limit.
In other words, find f(x), a, and b.
(Do not evaluate the limit or the integral.)
⌠ ⌡
b
a
f(x) dx =
lim
n→∞
n ∑
i=1
6
n
⎛ ⎝
10+
6i
n
⎞ ⎠
3
4. (2 pts.) Write the expression as a single integral in the form ∫ab f(x) dx.
⌠ ⌡
8
3
f(x) dx +
⌠ ⌡
20
8
f(x) dx −
⌠ ⌡
20
16
f(x) dx
5. (3 pts.) Evaluate the integral by interpreting it in terms of area.