Calc.II Problems

Sec. 7.2: Find the volume of the solid whose side is the region bounded by x=0, y=0, and y=4-2x; and the cross sections perpendicular to the given axis is the given shape. a) x-axis, squares b) y-axis, semi-circles	(need dpgraph for all links) The region a) The solid The solid with cross sections : Turn on scrollbar with variable A to move cross section. The region w/ cross sections : Turn on scrollbar with variable A to move cross section. The squares sweeping out the volume : Turn on scrollbar with variable A to move cross section. Volume = = b) The solid The Solid and midpoint sums : Turn on scrollbar with A to change number of half cylinders. The solid with cross sections : Turn on scrollbar with variable A to move cross section. The region w/ cross sections : Turn on scrollbar with variable A to move cross section. The semi-circles sweeping out the volume : Turn on scrollbar with variable A to move cross section. Volume = =
Sec. 7.2: Find the volume of revolution of the region bounded by y=Ln(x+1), x=2, and y=0 rotating about: a) x-axis b) y-axis c) x=3	(need dpgraph for all links) The region a) Revolving : Turn on scrollbar with variable A to form revolution. The solid of revolution The solid with disks : Turn on scrollbar with variable A to move disk. The disks w/ 2D graph : Turn on scrollbar with variable A to move disk. The disks sweeping out the volume : Turn on scrollbar with variable A to move cross section. Volume = = b) Revolving : Turn on scrollbar with variable A to form revolution. The solid of revolution The solid with washers : Turn on scrollbar with variable A to move washer. The washers w/ 2D graph : Turn on scrollbar with variable A to move washer. The washers sweeping out the volume : Turn on scrollbar with variable A to move cross section. Volume = = c) Revolving : Turn on scrollbar with variable A to form revolution. The solid of revolution The solid with washers : Turn on scrollbar with variable A to move washer. The washers w/ 2D graph : Turn on scrollbar with variable A to move washer. The washers sweeping out the volume : Turn on scrollbar with variable A to move cross section. Volume = =
Sec. 7.3: Find the volume of revolution of the region bounded by y=2x-x² and y=0 rotating about the y-axis.	(need dpgraph for all links) The region Revolving : Turn on scrollbar with variable A to form revolution. The solid of revolution The solid with shells : Turn on scrollbar with variable A to move shell. The shells w/ 2D graph : Turn on scrollbar with variable A to move shell. The shells sweeping out the volume: Turn on scrollbar with variable A to move shell. Volume = =
Sec. 7.4: Find the surface area of revolution of the function f(x)=sin(x) on [0,] rotating about the: a) x-axis b) y-axis	(need dpgraph for all links) The curve a) The surface The surface w/ circles : Turn on scrollbar with variable A to move circle. The circles w/ curve : Turn on scrollbar with variable A to move circle. Area = = b) The surface The surface w/ circles : Turn on scrollbar with variable A to move circle. The circles w/ curve : Turn on scrollbar with variable A to move circle. Area = =
Sec. 10.1:	See Sec. 6.1-6.3 in PreCalc.-Algebra.
Sec. 10.2: Demonstrate the use of parametric equations and the oscilloscope.	(need Winplot for this link) Graph
Sec. 10.4:	See Sec. 10.6 in Trigonometry.