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
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