Calculus II (MAT 146) Dr. Day Monday, January 29, 2018 Return Extended Homework A Integral Application #3: Volumes of Solids (6.2 and 6.3) Extended Homework A and Solutions For Next Time . . . Monday, January 29, 2018 MAT 146

Monday, January 29, 2018 MAT 146

Monday, January 29, 2018 MAT 146

Monday, January 29, 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 Monday, January 29, 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) Monday, January 29, 2018 MAT 146

Monday, January 29, 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. Monday, January 29, 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. Monday, January 29, 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. Monday, January 29, 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: Monday, January 29, 2018 MAT 146