7.1 Integration by Parts Fri April 24 Do Now 1)Integrate f(x) = sinx 2)Differentiate g(x) = 3x

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 #3-7, 17

7.1 Repeated Integration by Parts Mon April 27 Do Now Integrate by parts 1) 2)

HW Review: wkst p # ) 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 #

7.1 More Repeated Integration by Parts Tues April 28 Do Now Integrate by parts

HW Review: wkst p.567 # ) 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 Evaluateusing a different u and dv

Closure Hand in: Evaluate HW: (green) worksheet p.567 #13-16 Quiz Mon May 4

7.1 Tabular Integration Wed April 29 Do Now Integrate by parts

HW Review: p.567 # ) 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 Evaluateusing tabular integration

You try Evaluateusing tabular integration

Closure Hand in: Evaluateusing tabular integration HW: (green) worksheet p.567 # Quiz Mon May 4

7.1 Integration by Parts Practice Thurs April 30 Do Now Integrate using parts 1) 2)

HW Review: p.567 # ) 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 # Quiz Mon May 4

7.1 Integration by Parts Review Fri May 1 Do Now Integrate using tabular integration

HW Review: wkst p.520 # ) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

) 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 #7-25 odds, 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