1.The region R is the region bounded by the functions y=x-3 and x=1+y^2. find the volume of the solid obtained by rotating the region R about the y axis. Please include a graph.
2.Find the volume of the solid obtained by rotating the region bounded by the graphs of y=x and y=sqrt(x) about the line x=2. Please include a graph
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1.The region R is the region bounded by the functions y=x-3 and x=1+y^2. find the volume...
Find the volume of the solid obtained by revolving the region bounded by the graphs of the functions about the \(x\)-axis.Hint: You will need to evaluate two integrals. (Assume \(x>0 .\) )\(y=\frac{1}{x}, y=x_{r}\) and \(y=3 x\)By computing the volume of the solid obtained by revolving the region under the semicircle \(y=\sqrt{r^{2}-x^{2}}\) from \(x=-r\) to \(x=r\) about the \(x\)-axis, show that the volume of a sphere of radius \(r\) is \(\frac{4}{3} \pi r^{3}\), cublc units. (Do this by setting up the...
all answer Sample Test 4 1575 Calculus II 1. The region bounded by the parabola y-4x-x and the x -axis is revolved about thex- axis. Find the volume of the solid. Write answer in term of π. Find the area enclosed by the curves: 2. y=2x2-4x-12 y=x2-6x+12 and 3. Find the volume of the solid obtained by rotating the region bounded by the graphs of a. y-x-9, y 0 about the x-axis. -1 about the x-axis. b. y 16-r, y-3x+...
Consider the functions y = 6 - x?, y = 2. a. Graph the region bounded by these two curves. b. Find the volume of the solid obtained by rotating the region about the x-axis.
7) Find the volume of the solid obtained by rotating the region bounded byx (y-3)2 and x 4 about y 1. 7) Find the volume of the solid obtained by rotating the region bounded byx (y-3)2 and x 4 about y 1.
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the curves y=x^2, y=0, x=−2 and x=−1 about the y-axis.Volume = _______ Find the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.x^2+(y−7)^2=25about the x-axis. Volume = _______
1. Find the volume of the solid obtained by rotating the region bounded by the following curves about the horizontal line y=-3: y=6-x2,y-2, x = 1. 1. Find the volume of the solid obtained by rotating the region bounded by the following curves about the horizontal line y=-3: y=6-x2,y-2, x = 1.
Find the volume of the solid obtained by rotating the region bounded by y=r", y=0, x=1 about the y-axis. (a) ('(1 – VD? dy # [12 – (3y)?] dy (e) [ a[(79+1)2 – 1º) dy
please answer 1&2 Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x", y = 5x, x2 0; about the x-axis V = Sketch the region. y у 5- 6 4 3 3 N -0. 0.5 1.0 X 1.5 -0.5 0.5 1.0 1.5 Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 =...
Let R be the region bounded below by the graph of y=(x^2)+5 and above by the graphs of y=6x and y=12. Find the volume of the solid obtained by revolving R about the x-axis.
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y-7V36-,yo,x,x -2; about the x axis Sketch the region Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y-7V36-,yo,x,x -2; about the x axis Sketch the region