Unit 5 β Integration β Test 1 β Study Guide Concepts to know: 1. Finding anti-derivatives using the reverse-chain rule (with or without u-substitution) β must know trigonometric derivatives/integrals, as well as βeβ and ln. 2. Calculating definite integrals (including integrals calculated using geometric formulas) 3. Identifying an integral as a limit of a Riemann sum. 4. Motion problems with integration 5. Estimating Integrals using Riemann sums (LRAM, RRAM, MRAM, and Trapezoidal approximations.) Basic integrals that should be memorized: Reverse Power Rule: Critical Integrals to Know: ΰΆ± = ΰΆ± 1 = ΰΆ± = Evaluating a Definite Integral: ΰΆ± = β ΰΆ± β² = β or Where F is the anti-derivative of f
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Unit 5 Integration Test 1 Study GuideΒ Β· 2020. 1. 29.Β Β· The Definite Integral a Limit of a Riemann Sum Limit Statement Definite Integral lim πββ π=1 π (2+ 3 π π)2+2
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Unit 5 β Integration β Test 1 β Study Guide
Concepts to know:
1. Finding anti-derivatives using the reverse-chain rule (with or without u-substitution) β must know trigonometric derivatives/integrals, as well as βeβ and ln.
2. Calculating definite integrals (including integrals calculated using geometric formulas)
3. Identifying an integral as a limit of a Riemann sum.
4. Motion problems with integration
5. Estimating Integrals using Riemann sums (LRAM, RRAM, MRAM, and Trapezoidal approximations.)
Basic integrals that should be memorized:
Reverse Power Rule:
Critical Integrals to Know:
ΰΆ±ππ’ππ’ =
ΰΆ±1
π’ππ’ =
ΰΆ±π₯πππ₯ =
Evaluating a Definite Integral:
ΰΆ±
π
π
π π₯ ππ₯ = πΉ π β πΉ π ΰΆ±
π
π
πβ² π₯ ππ₯ = π π β π πor
Where F is the anti-derivative of f
Definite and Indefinite Integral PracticeIf U-sub doesnβt work, try algebraic manipulation and/or simplification
ΰΆ±π2π₯ sin π2π₯ β π ππ₯
Multiple Choice Released AP Questions β Definite and Indefinite Integrals
The Definite Integral as Area, and Integrals Using Geometric Formulas