1. 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

2. Monday, January 29, 2018
MAT 146

3. Monday, January 29, 2018
MAT 146

4. Monday, January 29, 2018
MAT 146

5. 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

6. 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

7. Monday, January 29, 2018
MAT 146

8. 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

9. 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

10. 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

11. 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