Download 5.6 Integration by Substitution

Chapter 5 section 6
1.  (x2  1)9 2x dx
7.  (2x2  4x)5 (x  1) dx
2.  ex 5x4 dx
x3  x2
8.  4
dx
3x  4x3
3.  (x4  16)5 x3 dx
9.
4.  e
e2x
10.  2x
dx
e 1
5
3x
dx
1
5.
 1  5x dx
6.

4
11.
x
1 x

2
dx
ln x
dx
x
12.  (x  1) x2 dx
x4  16 x 3 dx
13. BUSINESS: Cost – The weekly marginal cost of producing shoes is given by
C’ (x)
= 12 + 500/(x + 1) where C (x) is the cost in dollars. If the fixed cost are $2,000 per week, find
the cost function.
14. BUSINESS: Price-demand – The marginal price p’ (x) at x boxes of a certain cereal per
-.01x
week is given by p’ (x) = - 0.015e
. Find the price equation if the weekly demand is 50 boxes
when the price is $4.35.
15. MEDICINE – The rate of healing for a skin wound (in square centimeters per day) is
-0.1t
approximated by A’ (t) = - 0.9e
. If the initial wound has an area of 8 square centimeters,
what will its area be after t days? After 5 days?
16. POLLUTION - A contaminated lake is treated with a bactericide. The rate of
increase in harmful bacteria t days after the treatment is given by
dN
2000t

dt
1  t2
for 0  t  10
Where N (t) is the number of bacteria per milliliter of water.
a. Find the minimum value of dN/dt.
b. If the initial count was 5,000 bacteria per milliliter, find N (t).
c. Find the bacteria count after 10 days.