Objective Find an antiderivative using integration by parts Miss Battaglia AP Calculus If u and v are functions of x and have continuous derivatives then Integration by Parts Logs Inverse Trig ID: 578275
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Slide1
8-2 Integration by PartsObjective: Find an antiderivative using integration by parts.
Miss
Battaglia
AP CalculusSlide2
If u and v are functions of x and have continuous derivatives, then
Integration by PartsSlide3Slide4
LogsInverse TrigAlgebraic
Trig
Exponential
LIATESlide5
Derived from…Slide6
Try letting dv be the most complicated portion of the integrand that fits a basic integration rule. Then u will be the remaining factor(s) of the integrand.Try letting u be the portion of the integrand whose derivative is a function simpler than u. Then
dv
will be the remaining factor(s) of the integrand.
Note that dv always includes the dx of the original integrand.
Guidelines for Integration by PartsSlide7
FindIntegration by PartsSlide8
FindIntegration by PartsSlide9
FindAn Integrand with a Single TermSlide10
FindRepeated Use of Integration by PartsSlide11
FindIntegration by PartsSlide12
1. For integrals of the form
let
u =
xn
and let dv = eaxdx, sin ax dx, or cos
ax dx
2. For integrals of the form
let
u =
lnx
,
arcsin
ax
, or arctan ax and let dv = x
n
d
3. For the integrals of the form
let u = sin
bx
or
cos
bx
and let dv =
e
ax
dx
Summary of Common Integrals Using Integration by PartsSlide13
Read 8.2 Page 533 #11, 13, 15, 19, 27, 29, 32, 83, 99
Classwork/ Homework