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Integration
First some review…To integrate, you must have a sum/difference
or constant multiple combination of a variable to a number power (xn).
You may need to substitute one function for another in order to manipulate the integral to be in this form!
Integration finds net area between curves by accumulating heights.
Now you’re ready to play!Get into the following groups of students –
move your desks into these groups!!E. Yoder
D. Parker
K. Campbell
M. Flannery
J. Andrejko
R. Bauters
J. Jurado
D. Silva
G. Hucks
Now you’re ready to play!Designate one person in your group to “keep
score”. This person should draw a blank Tic-Tac-Toe board on a piece of paper. Keep track of which spaces you have filled in on this board by marking an X for the ones you get correct and an O for the ones do you not.
Remember: Your goal is to make three X’s across, down, or diagonally (just like in normal Tic-Tac-Toe). First group to accomplish this, wins 10 bonus points!
Choose one square of each type to make Tic-Tac-Toe…
Comprehension
Creative Thinking
Application
Creative Thinking
Application Comprehension
Application Comprehension
Creative Thinking
Comprehension
Integrate:
(Do not click the option below until EVERYONE has attempted the problem!)
Answer
Comprehension Answer
Discuss as a class why the answer is negative.Hint: Think about the location of the graph of
cosx between π/2 and π.Back to Game Board
Comprehension
Integrate:
(Do not click the option below until EVERYONE has attempted the problem!)
Answer
Comprehension Answer
Back to Game Board
82
82
1(0) 4
161
( 2) 416
840 4096
16
Comprehension
Integrate
(Do not click an option below until EVERYONE has attempted the problem!)
Answer
Comprehension Answer
Back to Game Board
Creative Thinking
Integrate
(Do not click the option below until EVERYONE has attempted the problem!)
Answer
Creative Thinking Answer
Back to Game Board
2
3 2
(3 2)
3 2
3 x du
u x
Creative Thinking
Integrate
(Do not click the option below until EVERYONE has attempted the problem!)
Answer
Creative Thinking Answer
Back to Game Board
Creative Thinking
Integrate
(Do not click the option below until EVERYONE has attempted the problem!)
Answer
Creative Thinking Answer
Back to Game Board
Recall…
2 20 2
3 32 2
2 0
x xx x
2 2( 2) 2
0 3( 2) 3(2) 02 2
( 8) 8 16
ApplicationThe graph of f(x) is shown:Calculate
(Do not click the option below until EVERYONE has attempted the problem!)
Answer
Application Answer Recall…the area above the x-axis is positiveand the area below the x-axis is negative in integration.
Using geometric shapes, divide thepositive region into a triangle from [-1,0], arectangle from [0,1], and a triangle from [1,2]. Add these up! 1+2+1 = 4
Subtract the triangular region from [2,3] and the rectangular region from [3,4]. 4-.5-1 = 2.5
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Application
The function f is continuous for all 1 < x < 7.
Approximate the value of using MRAM with 3 equal subdivisions.
(Do not click the option below until EVERYONE has attempted the problem!)
Answer
x 1 2 3 4 5 6 7f(x) 1 2 3.5 2 0 -1 0
Application Answer
Since we need 3 equal subdivisions, use:A1= the area from [1,3], ∆x = 2A2= the area from [3,5], ∆x = 2 and A3= the area from [5,7], ∆x = 2.
A1= (2)(f(2)) = 2(2) = 4A2= (2)( f(4))= 2(2) = 4A3= (2)( f(6)) = 2(-1) = -2
A1+ A2+ A3 = 4+4+-2 = 6.
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x 1 2 3 4 5 6 7f(x) 1 2 3.5 2 0 -1 0
ApplicationThe temperature T (in ˚C) recorded during a day
followed the curve where t is time and noon is t = 0. (In other words, for this day, -12 ≤ t ≤ 12.)
What was the average temperature during the day?
(Do not click the option below until EVERYONE has attempted the problem!)
Answer
Application Answer
For average temperature, “add up all the temperatures and divide by the number of temperatures accumulated.”
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