Integration Note Definite Integral

Integration Note Definite Integral




Math AA SL Concept Notes
Prepared by
Topic 5.10 & 5.11
Concepts covered:
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 Definite integral
 Review of integration rules
 Rules of definite integral
 Pastpaper practice
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,Integration


Integration rules recap:

1. Constant

ƒ 𝑘 𝑑𝑥 = 𝑘𝑥 + 𝐶


2. Power
𝑥n+1
ƒ 𝑥 𝑑𝑥 =
n + 𝐶, 𝑛 ≠ −1
𝑛+1
𝑘𝑥n+1
ƒ 𝑘𝑥 𝑑𝑥 =
n + 𝐶, 𝑛 ≠ −1
𝑛+1


Special case, 𝒏 = −𝟏:
1
ƒ 𝑑𝑥 = ln|𝑥| + 𝐶
𝑥


3. Exponential

ƒ 𝑒 x 𝑑𝑥 = 𝑒 x + 𝐶



4. Trigonometry

ƒ sin 𝑥 𝑑𝑥 = − cos 𝑥 + 𝐶

ƒ cos 𝑥 𝑑𝑥 = sin 𝑥 + 𝐶

, Integration


5. Composite function with 𝒂𝒙 + 𝒃

(A)
(𝑎𝑥 + 𝑏)n+1
ƒ(𝑎𝑥 + 𝑏) 𝑑𝑥 =
n + 𝐶, 𝑛 ≠ −1
𝑎(𝑛 + 1)


(B)
When 𝑛 = −1,
1 ln|𝑎𝑥 + 𝑏|
ƒ 𝑑𝑥 = +𝐶
𝑎𝑥 + 𝑏 𝑎


(C)
𝑒ax+b
ƒ 𝑒ax+ 𝑑𝑥 = +𝐶
𝑎


(D)
−cos(𝑎𝑥 + 𝑏)
ƒ sin(𝑎𝑥 + 𝑏) 𝑑𝑥 = +𝐶
𝑎
sin(𝑎𝑥 + 𝑏)
ƒ cos(𝑎𝑥 + 𝑏) 𝑑𝑥 = +𝐶
𝑎