l Integration Applications l Area Between Curves 6

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l Integration Applications l Area Between Curves (6. 1) l Average Value of a

l Integration Applications l Area Between Curves (6. 1) l Average Value of a Function (6. 5) l Volumes of Solids (6. 2, 6. 3) l Created by Rotations l Created using Cross Sections l U-substitution (5. 5) Integration by Parts (7. 1) l Trig Integrals (7. 2) l Trig Substitution (7. 3) l l Partial-Fraction Decomposition (7. 4) Friday, Sept 23, 2016 MAT 146

Friday, Sept 23, 2016 MAT 146

Friday, Sept 23, 2016 MAT 146

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? ? ? Friday, Sept 23, 2016 MAT 146

Friday, Sept 23, 2016 MAT 146

Friday, Sept 23, 2016 MAT 146

Improper Algebraic Fractions? Unfactorable Quadratics? Repeated Linear Factors? Friday, Sept 23, 2016 MAT 146

Improper Algebraic Fractions? Unfactorable Quadratics? Repeated Linear Factors? Friday, Sept 23, 2016 MAT 146

Consider the first-quadrant region R with borders y = sin(x) y = 0 and

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. (A) Calculate the exact area of R. Show evidence to support your solution. (B) 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, Sept 23, 2016 MAT 146

Consider the first-quadrant region R with borders y = sin(x) y = 0 and

Consider the first-quadrant region R with borders y = sin(x) y = 0 and (A) Sketch region R on the xy-plane. Friday, Sept 23, 2016 MAT 146 x = π/2

Consider the first-quadrant region R with borders y = sin(x) y = 0 and

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. Friday, Sept 23, 2016 MAT 146

Consider the first-quadrant region R with borders y = sin(x) y = 0 and

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: Friday, Sept 23, 2016 MAT 146