Math 128 Section 5.4 Interpretations of the Definite Integral
1
If () is a rate of change then:
Total change in quantity between t = a and t = b is ()
~
Ex: () represents the rate that the worlds population is changing
measured in millions of people per y
Math 128 Section 5.3 Definite Integral as Area
1
Integrals: Integrals, also called anti-derivatives, measure the net area
that a function makes with the x-axis (or the y-axis).
~
2
Area above the x-axis:
Area below the x-axis:
Ex: Does the value of the in
I. ' '
I k-bng-Bdow)x
(x +3 Kat4)
1=-3x=l a) ln(2:r) + C
b) (1113:) + c
4./x<z+'1)d=c= j xumx? SszerL-lx
a) E+w+0 ' - _
watt-+1):
4 +0
5)
c) $3+x2+0
d) (33:33)
afmm3=
a.) 232111231524'0 \
du.
b):r:21n:r:l-:1:2+C J.
E zalnxLmE-i-C
d) 32(lnz2)+C '
Math 128 Section 8.2 Cumulative Distribution Functions and Probability
1
Last Section: Density Functions (PDF or ()
This Section: Cumulative Distribution Functions (CDF or ()
CDF:
The shaded region represents the CDF.
() = ()
As , () 1
() is increasing (
Extra review questions for Exam 1
1. Find the area between y = 3x and y = x2 .
2. If f (t) is measured in pounds and x is measured in feet, what are the units of
Rb
a
f (x) dx?
3. The velocity of a particle (in m/s) is given by the graph below. What is th