unit 5 integration test 1 study guideย ยท 2020. 1. 29.ย ยท the definite integral a limit of a...
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![Page 1: Unit 5 Integration Test 1 Study Guideย ยท 2020. 1. 29.ย ยท The Definite Integral a Limit of a Riemann Sum Limit Statement Definite Integral lim ๐โโ ๐=1 ๐ (2+ 3 ๐ ๐)2+2](https://reader033.vdocuments.mx/reader033/viewer/2022061003/60b1871d5cd8824aa9103353/html5/thumbnails/1.jpg)
Unit 5 โ Integration โ Test 1 โ Study Guide
Concepts to know:
1. Finding anti-derivatives using the reverse-chain rule (with or without u-substitution) โ must know trigonometric derivatives/integrals, as well as โeโ 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:
เถฑ๐๐ข๐๐ข =
เถฑ1
๐ข๐๐ข =
เถฑ๐ฅ๐๐๐ฅ =
Evaluating a Definite Integral:
เถฑ
๐
๐
๐ ๐ฅ ๐๐ฅ = ๐น ๐ โ ๐น ๐ เถฑ
๐
๐
๐โฒ ๐ฅ ๐๐ฅ = ๐ ๐ โ ๐ ๐or
Where F is the anti-derivative of f
![Page 2: Unit 5 Integration Test 1 Study Guideย ยท 2020. 1. 29.ย ยท The Definite Integral a Limit of a Riemann Sum Limit Statement Definite Integral lim ๐โโ ๐=1 ๐ (2+ 3 ๐ ๐)2+2](https://reader033.vdocuments.mx/reader033/viewer/2022061003/60b1871d5cd8824aa9103353/html5/thumbnails/2.jpg)
Definite and Indefinite Integral PracticeIf U-sub doesnโt work, try algebraic manipulation and/or simplification
เถฑ๐2๐ฅ sin ๐2๐ฅ โ ๐ ๐๐ฅ
![Page 3: Unit 5 Integration Test 1 Study Guideย ยท 2020. 1. 29.ย ยท The Definite Integral a Limit of a Riemann Sum Limit Statement Definite Integral lim ๐โโ ๐=1 ๐ (2+ 3 ๐ ๐)2+2](https://reader033.vdocuments.mx/reader033/viewer/2022061003/60b1871d5cd8824aa9103353/html5/thumbnails/3.jpg)
Multiple Choice Released AP Questions โ Definite and Indefinite Integrals
![Page 4: Unit 5 Integration Test 1 Study Guideย ยท 2020. 1. 29.ย ยท The Definite Integral a Limit of a Riemann Sum Limit Statement Definite Integral lim ๐โโ ๐=1 ๐ (2+ 3 ๐ ๐)2+2](https://reader033.vdocuments.mx/reader033/viewer/2022061003/60b1871d5cd8824aa9103353/html5/thumbnails/4.jpg)
The Definite Integral as Area, and Integrals Using Geometric Formulas
เถฑ
โ4
0
16 โ ๐ฅ2๐๐ฅ เถฑ
2 2
โ2 2
8 โ ๐ฅ2 + 3 ๐๐ฅ
![Page 5: Unit 5 Integration Test 1 Study Guideย ยท 2020. 1. 29.ย ยท The Definite Integral a Limit of a Riemann Sum Limit Statement Definite Integral lim ๐โโ ๐=1 ๐ (2+ 3 ๐ ๐)2+2](https://reader033.vdocuments.mx/reader033/viewer/2022061003/60b1871d5cd8824aa9103353/html5/thumbnails/5.jpg)
The Definite Integral a Limit of a Riemann Sum
Limit Statement Definite Integral
lim๐โโ
๐=1
๐
(2 +3
๐๐)2+2 โ
3
๐
lim๐โโ
๐=1
๐
3(2
๐(๐ โ 1) + 6 โ
2
๐
lim๐โโ
๐=1
๐
2(4 +5
๐๐)3 + 6 โ
5
๐
lim๐โโ
๐=1
๐
4 โ (1
๐๐)2 โ
1
๐
lim๐โโ
๐=1
๐
sin(3 +7
๐(๐ โ 1) โ
7
๐
Definite Integral Limit Statement
เถฑโ1
2
(๐ฅ2 โ 6)๐๐ฅ
เถฑ1
9
(5๐ฅ + 4)๐๐ฅ
![Page 6: Unit 5 Integration Test 1 Study Guideย ยท 2020. 1. 29.ย ยท The Definite Integral a Limit of a Riemann Sum Limit Statement Definite Integral lim ๐โโ ๐=1 ๐ (2+ 3 ๐ ๐)2+2](https://reader033.vdocuments.mx/reader033/viewer/2022061003/60b1871d5cd8824aa9103353/html5/thumbnails/6.jpg)
Motion Problems Utilizing Integration
![Page 7: Unit 5 Integration Test 1 Study Guideย ยท 2020. 1. 29.ย ยท The Definite Integral a Limit of a Riemann Sum Limit Statement Definite Integral lim ๐โโ ๐=1 ๐ (2+ 3 ๐ ๐)2+2](https://reader033.vdocuments.mx/reader033/viewer/2022061003/60b1871d5cd8824aa9103353/html5/thumbnails/7.jpg)
Rectangular and Trapezoidal Approximations
![Page 8: Unit 5 Integration Test 1 Study Guideย ยท 2020. 1. 29.ย ยท The Definite Integral a Limit of a Riemann Sum Limit Statement Definite Integral lim ๐โโ ๐=1 ๐ (2+ 3 ๐ ๐)2+2](https://reader033.vdocuments.mx/reader033/viewer/2022061003/60b1871d5cd8824aa9103353/html5/thumbnails/8.jpg)