Integration
By Jason Leitmeyer, Shannon Hunt, Doris Bittner
OutlineIndefinite IntegralsDefinite IntegralsUsing Integration to Find Area
◦Total Area◦Net Signed Area
Rectilinear Motion Using Integration◦Position, Velocity, Speed,
Acceleration
Indefinite IntegralsIntegral Power Rule
A constant factor can be moved through an integral sign
cr
xdxx
rr
1
1
dxxfcdxxcf )()(
Indefinite Integrals (cont.)Examples1)
2)
dxxx )1( 3
dxx
xx
4
25 12
Indefinite Integrals (cont.)
dxex
x )32(
dxex x322
3)
4)
5) tdtt 3sin3cos4
Definite Integrals
dxxx9
4
2 *
dxxx32
0
2 1
dxx
5.
5. 21
1
Definite Integrals (cont.)
dxxx 2cos2sin8
0
5
dxx
x 8
0 3
2
9
Rectilinear Motion using integrationFind the position function for a
particle3)0(,sin1)( sttV
v(0)=0 s(0)=0
13ta(t) 2 t
Rectilinear MotionSigned Area – plug into
calculator
24
1
2 x
Total Area-
b
adxxf )( Plug into calculator
Find the total area between the curve Y=sinx and the x-axis over the interval [0,2π]
Computing Displacement and Velocity by Integration
)sin()( tta
10 v
2
2
4
2t
Computing Displacement and Velocity by Integration (cont.)Find the position, velocity, speed
and acceleration at time t=π if v(t)=cos(t) s(0)=1
Computing Displacement and Velocity by Integration (cont.)Find the position function for a
particle
v(0)=0 s(0)=0
13ta(t) 2 t
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