1. Calculus II (MAT 146) Dr. Day Friday, February 2, 2018
Volumes of Solids with Known Cross Sections (6.2 & 6.3)
Quiz #5 Today!
Return to Methods of Integration (Ch 7)
Integration Method #2: Integration by Parts (7.1)
Test #1: Friday, Feb 9: STV 211
Friday, February 2, 2018
MAT 146

2. Friday, February 2, 2018
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3. Friday, February 2, 2018
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4. Friday, February 2, 2018
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5. Volumes of Solids of Revolution (6.2 & 6.3)
Dynamic Illustration #1 (discs)
Dynamic Illustration #2 (washer)
Dynamic Illustration #3 (shell)
Dynamic Illustration #4 (cross section I) (cross section II)
Friday, February 2, 2018
MAT 146

6. Region R in the first quadrant of the xy-plane is bordered by the x-axis, the line x = 4, and the curve y = √x.
Determine the volume of the solid of revolution generated when R is rotated about the line y = 2.
Determine the volume of the solid of revolution generated when R is rotated about the line x = −1.
(A) (8pi)/3 (B) (544pi)/15
Friday, February 2, 2018
MAT 146

7. Friday, February 2, 2018
MAT 146

8. Consider the first-quadrant region R with borders
y = sin(x) y = 0 and x = π/2
Sketch region R on the xy-plane.
Calculate the exact area of R. Show evidence to support your solution.
Set up, but do not calculate, a definite integral to represent the volume of the solid created when R is revolved around the y-axis.
Set up, but do not calculate, a definite integral to represent the volume of the solid created when that solid is built on a base R with cross sections, perpendicular to the x-axis, that are semi-circles.
Friday, February 2, 2018
MAT 146

9. Consider the first-quadrant region R with borders
y = sin(x) y = 0 and x = π/2
Sketch region R on the xy-plane.
Friday, February 2, 2018
MAT 146

10. Consider the first-quadrant region R with borders
y = sin(x) y = 0 and x = π/2
Calculate the exact area of R. Show evidence to support your solution.
Friday, February 2, 2018
MAT 146

11. Consider the first-quadrant region R with borders
y = sin(x) y = 0 and x = π/2
Set up, but do not calculate, a definite integral to represent the volume of the solid created when R is revolved around the y-axis.
Shells:
Washers:
Friday, February 2, 2018
MAT 146

12. Consider the first-quadrant region R with borders
y = sin(x) y = 0 and x = π/2
Set up, but do not calculate, a definite integral to represent the volume of the solid created when that solid is built on a base R with cross sections, perpendicular to the x-axis, that are semi-circles.
Friday, February 2, 2018
MAT 146

13. MAT 146

14. Undoing the Product Rule
Friday, February 2, 2018
MAT 146

15. Integration by Parts Key Component of Integrand’s Two Factors
For at least one factor, its derivative is “simpler” than the factor.
For at least one factor, its anti-derivative is no more complex than the factor.
Friday, February 2, 2018
MAT 146

16. Friday, February 2, 2018
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17. You Choosing U: A Decision Algorithm
L: log functions I: inverse trig functions A: algebraic functions T: trig functions E: exponential functions
MAT 146
Friday, February 2, 2018

18. Review: Derivatives of Inverse Trig Functions
Friday, February 2, 2018
MAT 146

19. Derivatives of Inverse Trig Functions: Co-Function Connections
Friday, February 2, 2018
MAT 146

20. Trig Integrals
Friday, February 2, 2018
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21. More Trig Integrals!
Friday, February 2, 2018
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22. Which Roots Can You Simplify Mentally?
Friday, February 2, 2018
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23. Pythagorean Trig Identities
Friday, February 2, 2018
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24. Integrals Begging for Trig Substitutions!
Friday, February 2, 2018
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25. Using Trig Substitutions
Friday, February 2, 2018
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26. Trig Substitutions
Friday, February 2, 2018
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27. Integration Strategies: Which of These Can You Evaluate, WITHOUT Your CAS?
Friday, February 2, 2018
MAT 146

28. Partial-Fraction Decomposition
??????
Friday, February 2, 2018
MAT 146

29. Partial-Fraction Decomposition
Friday, February 2, 2018
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30. What About… Improper Algebraic Fractions? Unfactorable Quadratics?
Repeated Linear Factors?
Friday, February 2, 2018
MAT 146