Agenda: Feb. 4• HW Check• Practice• 7.1 Integration overview

Quote of the Day: "After years of finding mathematics easy, I finally reached integral calculus and came up against a barrier. I realized that this was as far as I could go, and to this day I have never successfully gone beyond it in any but the most superficial way." -- Isaac Asimov

Integration Formulas:p. 484 The “Biggies”

Inverse trig Inegrals

Integration Techniques p. 4851) Separate numerator

2) Complete the square

3) Add/subtract terms in numerator

4) Expand

5) Divide improper rational functions

6) Trig identities

7) Multiply/divide Pythagorean conjugate

Integration tip: try u-sub firstExample using: • add/subtract what’s missing , • separate numerator, complete the square

∫ 2 𝑥𝑥2+6 𝑥+13

𝑑𝑥

Example using: • add/subtract what’s missing• Separate numerator

∫ 11+𝑒𝑥 𝑑𝑥

4) Expand

∫ (𝑥+1 )2

𝑥 𝑑𝑥

5) Divide Improper Rational

∫ 𝑥2

𝑥2+1𝑑𝑥

6. Trig Identities (more in Sec 7.3)

∫ tan (𝑥 ) 𝑑𝑥

6. Trig Identities (more in Sec 7.3)

∫ sec (𝑥 )𝑑𝑥

7. Pythagorean conjugate

∫ 11+sin (𝑥)

𝑑𝑥

Similar but different

Log Forms and substitution

HOMEWORK 19p. 486 ## 21, 25-33(odd), 39, 43,45, 49, 51, 55, 56, 57, 61, 67, 69

Challenge Problem – due Friday