1. Seating by Group
Thursday, September 1, 2016
MAT 146

2. Calculus II (MAT 146) Dr. Day Thursday September 1, 2016
Integral Applications:
Area Between Curves (6.1)
Average Value of a Function (6.5)
Volumes of Solids: Rotations and Cross Sections (6.2, 6.3)
Assignments: WebAssign 6.5, 6.2
Quiz #3: Calculus I Chs 3/4/5 Review
Mathematics Department Picnic!
Sunday, Sept 11, 4:30-7:30
Underwood Park
Free Food for Undergrads!
Thursday, September 1, 2016
MAT 146

3. The average value of a function f, on a ≤ x ≤ b, with f continuous on that interval, is:
Thursday, September 1, 2016
MAT 146

4. 1) Calculate the average value of the function whose graph is shown here, on 0 ≤ x ≤ 8.
2) Approximate any values of x at which the function actually takes on its average value.
Friday, January 22, 2016
MAT 146

5. Friday, January 22, 2016
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6. Friday, January 22, 2016
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7. Friday, January 22, 2016
MAT 146

8. 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, January 22, 2016
MAT 146

9. 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, January 22, 2016
MAT 146

10. Friday, January 22, 2016
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11. 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.
Friday, January 22, 2016
MAT 146

12. 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, January 22, 2016
MAT 146

13. 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, January 22, 2016
MAT 146

14. 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, January 22, 2016
MAT 146

15. Undoing the Product Rule
Friday, January 22, 2016
MAT 146

16. 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, January 22, 2016
MAT 146

17. Friday, January 22, 2016
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18. 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, January 22, 2016