17
Calculus II (MAT 146) Dr. Day Monday, Feb 16, 2015 Partial Fraction Decomposition (7.4) Improper Integrals (7.8) Assignments Monday, February 16, 2015 MAT 146

Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

Embed Size (px)

Citation preview

Page 1: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

Calculus II (MAT 146)Dr. Day Monday, Feb 16, 2015

Partial Fraction Decomposition (7.4)

Improper Integrals (7.8)

Assignments

Monday, February 16, 2015

MAT 146

Page 2: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Partial-Fraction Decomposition

Monday, February 16, 2015

??????

Page 3: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Partial-Fraction Decomposition

Monday, February 16, 2015

Page 4: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

What About…

Monday, February 16, 2015

Improper Algebraic Fractions?

Unfactorable Quadratics?

Repeated Linear Factors?

Page 5: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Improper Integrals (7.8)

Monday, February 16, 2015

Page 6: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Improper Integrals (7.8)

Monday, February 16, 2015

Page 7: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Improper Integrals (7.8)

Monday, February 16, 2015

Page 8: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Improper Integrals (7.8)

Monday, February 16, 2015

Page 9: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Improper Integrals (7.8)

Monday, February 16, 2015

Page 10: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

WebAssign 7.4 Homework due tonight! 7.5 Homework due tonight! 7.8 Homework due Wednesday 2/18

Assignments

Monday, February 16, 2015

Page 11: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146Monday, February 16, 2015

Consider the first-quadrant region R with borders

y = sin(x) y = 0 and

x = π/2

(A)Sketch region R on the xy-plane.

(B)Calculate the exact area of R. Show evidence to support your solution.

(C)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.

Page 12: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146Monday, February 16, 2015

Consider the first-quadrant region R with borders

y = sin(x) y = 0 and

x = π/2

(A)Sketch region R on the xy-plane.

Page 13: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146Monday, February 16, 2015

Consider the first-quadrant region R with borders

y = sin(x) y = 0 and

x = π/2

B. Calculate the exact area of R. Show evidence to support your solution.

Page 14: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146Monday, February 16, 2015

Consider the first-quadrant region R with borders

y = sin(x) y = 0 and

x = π/2

C. 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:

Page 15: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Trig Integrals:Which is Easiest?

Toughest?

Monday, February 16, 2015

Page 16: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Review: Derivatives of Inverse

Trig Functions

Monday, February 16, 2015

Page 17: Monday, February 16, 2015MAT 146. Monday, February 16, 2015MAT 146

MAT 146

Derivatives of Inverse Trig

Functions:

Co-Function Connections

Monday, February 16, 2015