MTH 1260
Worksheet #4
(1) Calculate the following integrals.
(a) Z(x2−5x)4(2x−5) dx
(b) Z1
0
ex√ex+ 1 dx
(c) Z√x(1 + 2x)dx
(d) Z5
3
3x
√x−2dx (Use the substitution u=x−2.)
(e) Zxe−xdx (Use integration by parts.)
(2) The rate of infection of a disease (in people per month) is given by the function
I0(t) = 100t
t2+ 1, where tis the time in months since the disease broke out. Find the
total number of infected people during the first four months of the disease.
(3) A region Ris enclosed by the curves y=xand y=x2. Find the area of R.
(4) Suppose the temperature in a river at a point xin meters downstream from a factory
that is discharging hot water into the river is given by T(x) = 400 −0.25x2. Find
the average temperature over the interval [10,40].