Consider the region bounded by the curves y= (x)/(1-x) , x= 0, x=(1/2), y=0. Calculate the volume of the solid that is created when this region is revolved about the x-axis. Homework Equations The Attempt at a Solution This is the work I have so far, but it seems to be...
Answer to: Find the volume of the following solid. The region bounded by y = \frac{1}{x+3} , y = 0, x = 0, and x = 7 is revolved around the...
Find the volume of the solid generated by revolving the shaded region about the x-axis. Volume of Solid of Revolution: Since the region is being revolved around the {eq}x{/eq}-axis thus the easier method to use is the disc method which has the formula {eq}V=\pi...
Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^2 + 2x, y = 0, x = 0, and x = 1 around the y-axis. Find the volume of the solid formed by revolving the region boun...
= area revolved around the y axis. There are three ways to find this volume. We can do this by (a) using volume formulas for the cone and cylinder, (b) integrating two different solids and taking the difference, or (c) using shell integration (rotating an area around a different axis...
Find the volume of the solid generated by revolving the region bounded by y=x \sin x; 0 \leq x \leq \pi about the x-axis. Find the volume of the solid formed by revolving the region bounded by y = x, y = x^3, x = 0, x = ...
Answer(2) The curve y=2x−x2y=2x−x2 bounded by y=0y=0, revolved about the xx-axis.Answer(3) The curve y2=xy2=x, bounded by y=4y=4 and x=0x=0, revolved about the yy-axis.Answer(4) The curve x2+4y2=4x2+4y2=4 in quadrant I, revolved around the yy-axis.Answer...
Shell method formula When we have a continuous and nonnegative function, f(x), over the interval of [a,b], we can rotate the region under its curve around the y-axis and end up with a solid made up of cylindrical shells that have the following dimensions: ...
Notice that when each line segment is revolved around the axis, it produces a band. These bands are actually pieces of cones (think of an ice cream cone with the pointy end cut off). A piece of a cone like this is called a frustum of a cone. To find the surface area of...
Use the shell method to find the volume for {eq}y = -x^2 + 4x + 2 {/eq} and {eq}y = x^2 - 6x + 10 {/eq} revolved around the y-axis. Finding the Volume: We need to find the volume of the solid by using the Shel...