7.1 Integration by PartsFri April 24

Do Now

1) Integrate f(x) = sinx

2) Differentiate g(x) = 3x

6.2 6.3 Quiz Review

• Retakes by next Wed

Integration by Parts

• Let f(x) be a function that is a product of two expressions u and dv.

• Then,

How do we choose U?

• There are a couple of acronyms used to choose a U-expression

• L – Logarithmic

• A - Algebraic (polynomials)

• T - Trigonometric

• E - Exponential

Integration by Parts

• 1) Identify u

• 2) Identify dv

• 3) Find du

• 4) Find v by evaluating

• 5) Plug into parts formula and evaluate

• Note: Don’t forget the + C

Ex 2.1

• Evaluate

Ex 2.1b

• What happens when we choose the wrong u and dv?

Ex 2

• Evaluate

Ex 2.3

• Evaluate

Closure

• Hand in: Integrate by parts

• HW: (green) worksheet p.566-567 #3-7, 17

7.1 Repeated Integration by Parts

Mon April 27• Do Now

• Integrate by parts

• 1)

• 2)

HW Review: wkst p.566-567 #3-7 17

• 3)

• 4)

• 5)

• 6)

• 7)

• 17)

Repeated Integration by Parts

• The more complicated the function, the more likely we will have to repeat integration by parts

• Note: The 2nd integration by parts should be a simpler expression

Ex 2.4

• Evaluate

More ex

• From book (if needed)

Closure

• Hand in: Integrate by parts repeatedly

• HW: (green) worksheet p.567 #9 11 12 19 20

7.1 More Repeated Integration by Parts

Tues April 28• Do Now

• Integrate by parts

HW Review: wkst p.567 #9 11 12 19 20

• 9)

• 11)

• 12)

• 19)

• 20)

Manipulation with Parts

• Sometimes regardless of how we choose u and dv, we obtain an integral that is similar to the original

• This usually happens when there is both an exponential AND a trig function

Ex 2.5

• Evaluate

Ex 2.5

• Evaluate using a different u and dv

Closure

• Hand in: Evaluate

• HW: (green) worksheet p.567 #13-16

• Quiz Mon May 4

7.1 Tabular IntegrationWed April 29

• Do Now

• Integrate by parts

HW Review: p.567 #13-16

• 13)

• 14)

• 15)

• 16)

Tabular Integration

• Tabular integration is a method of integration by parts that can be used when having to repeat parts many times

• Tabular integration only works if u is an algebraic expression (ex: x^4)

Tabular Integration

• 1) Choose u and dv and create a table, placing dv one row above u

• 2) Differentiate u in a column until you get 0

• 3) Integrate dv in a column until every u has a partner.

• 4) In a 3rd column, alternate signs• 5) Match up each u and v

Ex

• Evaluate using tabular integration

You try

• Evaluate using tabular integration

Closure

• Hand in: Evaluateusing tabular integration

• HW: (green) worksheet p.567 #52 53 55 56

• Quiz Mon May 4

7.1 Integration by Parts Practice

Thurs April 30• Do Now

• Integrate using parts

• 1)

• 2)

HW Review: p.567 #52 53 55 56

• 52)

• 53)

• 55)

• 56)

Practice

• (blue) Worksheet p. 520 #1-11, 19-20, 43-45

Closure

• Journal Entry: When using integration by parts, what makes a good u and dv? What expressions would we want to choose as u?

• HW: Finish worksheet p.520 #1-11 19 20 43-45

• Quiz Mon May 4

7.1 Integration by Parts Review

Fri May 1• Do Now

• Integrate using tabular integration

HW Review: wkst p.520 #1-11 19-22 43-45• 1) • 2)• 3)• 4)• 5)• 6)• 7)• 8)• 9)• 10)• 11)

19-22 43-45• 19)

• 20)

• 21)

• 22)

• 43)

• 44)

• 45)

Quiz Review

• Integration by Parts– Single Integration by Parts– Repeated Integration

• Repeat parts, or use tabular if possible

– No bounds• Remember LATE

Practice worksheet

• (green) worksheet p.567 #25-32 no bounds

• Also try textbook p.403-404 #7-25 odds, 49-53 odds

Closure

• Journal Entry: When using integration by parts on a high degree function, would you rather repeat integration by parts, or use tabular integration? Why? If you had to explain a problem to another student, which technique would you use?

• HW: Study for quiz Monday