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Lecture 21

# MATA32H3 Lecture 21: MATA32H3-Lec21-Integration and AntiderivationPremium

Department
Mathematics
Course Code
MATA32H3
Professor
Karimian Pour, C.
Lecture
21

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MATA32H3-Lec21-Integration and Antiderivation
Integration Examples
1. f(x)= 5sqrt(x) = 5x^2
5x^(1/2)dx = 5 (3/2 x^(3/2)) + C
(10/3 x^(3/2) + C) = (10/3) (3/2 x^(1/2))
= 5x^(1/2)
2. β«(1/π₯)dx = ln (x) + C
Reason: (d/dx) ln(x) + C = (1/x)
3. β«lnβ‘(π₯)dx = x ln(x) β x + C
Check by differentiation
(d/dx) [x ln(x) β x + C] = ln(x) + x(1/x) β 1
= ln(x) + 1 β 1
= ln(x)
β’ β«π₯^π dx = ((x^(n+1))/(n+1)) + - C , n cannot equal -1
β’ β«(1/π₯) dx = ln(x) + C
β’ β«π^π‘ dt = e^t + C
β’ β«[ππ(π₯)β‘dx] = k [β«π(π₯)dx]
β’ β«[π(π₯)+β‘ββ‘π(π₯)]β‘ ππ₯ = β«π(π₯) dx + - β«π(π₯) dx
WARNING:
β«π(π₯)π(π₯)]β‘ ππ₯ does not equal β«π(π₯) dx β«π(π₯) dx