Area
Antiderivatives
Definite Integrals and Total Area
More Antiderivatives
Concepts
100
As more rectangles are added to find the area under the curve, the area represented by the rectangles will_________ compared to the true area
get closer
100
x2-12x+15
(x3/3)-6x2+15x+C
100
This type of area cannot be negative
total area
100
14ex
14ex+C
100
If you are shown a rate of change of graph showing how many books are ordered per year starting in 2015, what would the label on the integral be?
Books ordered (since 2015)
200
Using the graph on the board find the singed area
160
200
5/x
5 ln (x)+ C
200
Find the definite integral
f(x)= -4x-2 ; a=1, b=4
-3
200
e14x
e14x/14+c
200
What is the first step in solving for an integral algebraically?
Vertical Bar Notation
300
Using the function f(x)= -.25x2+2x+10
Find the height of the second right rectangle if you want to find the area from 0-9 using 3 rectangles
f(6)=13
300
Find the Specific Antiderivative
f(z)=z-2+8z; F(2)=5
-z-1+8z2/2-10.5
300
Find the Total Area
f(x)= -4x-2 ; a=1, b=4
3
300
Find the specific antiderivative
f(x)= x-2 + ex ; F(2)=1
F(2)= 1= -2-1+ e2+c
c= 1.5 + e2
300
What do inflection points on an accumulation graph mean on the related rate of change graph?
Relative Mins/Maxs
400
Find the accumulated area at 47 when you start at0.
A=40.4
400
x-2(x4-7x2-9)
x3/3-7x-9x-1
400
Find the definite integral. (Round to 3 decimals)
f(x)= 9.295x-1 -1.472; a=0.5, b=3.5
-0.917
400
2x-1+.38(.1x)
0.8 ln x + 0.38(0.1x)/ ln 0.1+C
400
When interpreting a definite integral, if the area is positive then the rate of change...
increased
500
Find the Total Area of the graph from 0 to 47
A=71.2
500
(5x4-2x3)/x5
5ln(x)+2x-1
500
f(x)= 9.295x-1 -1.472; a=0.5, b=3.5
1.386
500
The rate of change of the weight of a mouse can be modeled as: w(t)= 7.37t-1 grams per week, where t is the age of the mouse, in weeks, beyond two weeks. At an age of 9 weeks, the mouse weighed 26 grams.
Find the Specific Antiderivative
W(t)= 7.37 ln t + 11.6586 grams
500
Using the graph x2, when would the graph be increasing/decreasing, and is it increasing faster or slower in these areas?
negative infinity to 0= decreasing slower
0 to infinity= increasing faster