Calculus II (MAT 146) Dr. Day Wednesday, January 31, 2018

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Presentation transcript:

Calculus II (MAT 146) Dr. Day Wednesday, January 31, 2018 Continue Integral Application #3: Volumes of Solids (6.2 & 6.3) Solids of Revolution Solids with Known Cross Sections For Next Time . . . Quiz #5 on Friday! Coming Up: Returning to Methods of Integration (Ch 7) Test #1: Friday, Feb 9: STV 211 Wednesday, January 31, 2018 MAT 146

Wednesday, January 31, 2018 MAT 146

Wednesday, January 31, 2018 MAT 146

Wednesday, January 31, 2018 MAT 146

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) Wednesday, January 31, 2018 MAT 146

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 Wednesday, January 31, 2018 MAT 146

Wednesday, January 31, 2018 MAT 146

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. Wednesday, January 31, 2018 MAT 146

Consider the first-quadrant region R with borders y = sin(x) y = 0 and x = π/2 Sketch region R on the xy-plane. Wednesday, January 31, 2018 MAT 146

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. Wednesday, January 31, 2018 MAT 146

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: Wednesday, January 31, 2018 MAT 146