. Choose the one alternative that best completes the statement or answers the question.
Evaluate using integration by parts.
1) ln 4x dx
2)
Illustrate the integral graphically and describe what the integral represents in terms of areas.
3)
A) The integral represents the area between
the graph of y = (x - 3) and the x axis
from x = 0 to x = 1.
B) The integral represents the negative of the
area between the graph of y = (x - 3) and
the x axis from x = 0 to x = 1.
C) The integral represents the negative of the
area between the graph of y = (x - 3) and
the x axis from x = 0 to x = 1.
D) The integral represents the area between the
graph of y = (x - 3) and the x axis from
x = 0 to x = 1.
Use a graphing calculator to graph the equation over the indicated interval and find the area between the curve and
the x axis over that interval. Find the answer to two decimal places.
4) y = x - 4 - ln x; 1 ≤ x ≤ 8
Solve the problem.
5) After a person takes a pill, the drug contained in the pill is assimilated into the bloodstream. The rate of assimilation
minutes after taking the pill is Find the total amount of the drug that is assimilated into the bloodstream
during the first 15 minutes after the pill is taken. Round your answer to 2 decimal places.
Use the Trapezoidal Rule to approximate the integral using the indicated value of n.
6) ; n = 4, Write answer as a whole number or reduced fraction.
Use Simpson's rule to approximate the integral using the indicated value of n (so there are 2n subintervals).
7) ; n = 4, Round to three decimal places.
8) dx; n = 4, Round to two decimal places.
Find the indefinite integral using a table of integration formulas.
9) dx
10)
11) dx
Solve the problem.
12) The rate of growth of a microbe population is given by m'(x) = 30 x , where x is time in days. What is the net
growth between day 3 and day 7?