49. Use the method of shells to find the volume of the donut created when the circle x2+y2=4x2+y2=4 is rotated around the line x=4.x=4. 50. Consider the region enclosed by the graphs of y=f(x),y=1+f(x),x=0,y=0,y=f(x),y=1+f(x),x=0,y=0, and x=a>0....
On the last time,you have known what a right circular cylinder is in calculus.Right circular cylinders are just a part of solids of revolution.Today you will learn solids of revolution aren t right circular cylinders.In general way,a solid is bounded by the region under the curve y=f(x)...
3. Measuring volume of solids of known cross-sectional area:∫A(x) dx 4. Measuring volume of solids of revolution:∏∫[R(x)]^2 dx,∏∫([R(x)]^2-[r(x)]^2) dx 5. Arc length of function graphs: s=∫√(1+f’(x)^2) dx, s=∫√(1+g’(y)^2) dy 6. Surface area of ...
Skills Review for Area Between Two Curves, Determining Volumes by Slicing, and Volumes of Revolution: Cylindrical ShellsLearning OutcomesGraph horizontal and vertical lines Graph linear equations in different forms using ordered pairs Graph a linear equation using x and y-intercepts Determine if and ...
4 Ch3 The applications of Integral calculus 积分学的应用 3.1 The applications of definite integral: the area of a plane region-平面图形的面积 3.2 The applications of definite integral: the volume of solid of revolution 旋转体的体积 3.3 The volume of Mouhefanggai 牟合方盖 3.4 The applications...
cylindrical shell method: A procedure for finding the volume of a solid of revolution by treating it as a collection of nested thin rings. 圆柱壳法:通过将旋转实体视为嵌套的细环的集合来查找旋转体的体积的过程。 differentiable: A function is said to be differentiable at a point when the functi...
The VolumeOfRevolutionTutor displays the plot, interval, and area of the volume of revolution of a function where the axis of revolution can be either the horizontal or vertical axis. The corresponding Maple command is displayed in the bottom of the maplet application. Copy this command from the...
7. One of the most difficult concepts for me as a student of calculus was finding the volume of solids. If students cannot visualize the solids, they have a moredifficult timeunderstanding how to compute thevolume. To enable students to“see” the solids of revolution, I have purchased sever...
2.1.1 Definition of a sequence(36) 2.1.2 Descriptive definition of limit of a sequence(36) 2.1.3 Quantitative definition of limit of a sequence(38) 2.2 Limits of functions(39) 2.2.1 Definition of finite limits of functions as x→x0(39) ...