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AP Calculus AB
Partial Fractions & Improper/Discontinuous Integrals
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Calculus
Integration
AP Calculus AB
11th
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19 Terms
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Integration by Parts
∫udv= uv-∫vdu
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What does LIPET tell you
The order of priority for choosing u
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What is L in LIPET
logs
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What is I in LIPET
inverse trig
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What is P in LIPET
polynomials
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What is E in LIPET
exponentials
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What is T in LIPET
trig
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How do you apply Partial Differention?
1) If n≥d, start w/ long÷
2) Factor denominator
3) Write equation w/ original integrand on left & fraction for ea. factor on right
4) Solve for all numerators (mult. both sides by LCD)
5) Rewrite original integral & evaluate
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What are improper integrals?
Integrals that have ∞
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∫a to ∞ f(x)dx
lim b→∞ ∫a to b f(x)dx
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∫-∞ to b f(x)dx
lim b→-∞ ∫a to b f(x)dx
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∫-∞ to ∞ f(x)dx
∫-∞ to a f(x)dx + ∫a to ∞ f(x)dx
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Convergent
real number
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divergent
\-∞ & ∞
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Discontinuous integrals
integrals with a vertical asymptote
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∫a to b f(x)dx
lim t→b⁻ ∫a to t f(x)dx (VA at x=b)
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∫a to b f(x)dx
lim t→a+ ∫t to tbf(x)dx (VA at x=a)
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∫a to b f(x)dx
∫a to c f(x)dx + ∫c to b f(x)dx (VA is between a&b)
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When can we use Tab Method?
When we have an integral that’s the product of a polynomial w/ an exponential, sin or cos func, or e