50. Find the volume swept out by revolving the region bounded by the y-axis and the graph of x=1(1-1), y=1+12 50. Find the volume swept out by revolving the region bounded by the y-axis and the...
50. Find the volume swept out by revolving the region bounded by the y-axis and the graph of x=1(1-1), y=1+12
volumes of revolution 3) Find the volume of the solid formed by revolving the region bounded by the graphs of y- x+1, y +1, x 0, and x-1 about the x-axis. 3) Find the volume of the solid formed by revolving the region bounded by the graphs of y- x+1, y +1, x 0, and x-1 about the x-axis.
4. Find the volume of the solid formed by revolving the region bounded by the graphs of y=r3, = 2 and y=1 about the y-axis 5. Find volume of the solid formed by revolving the region bounded by the graphs of y=x, y=1 and x = 2 about the line y = 10 6. Find the volume of the solid formed by revolving the region bounded by the graphs of y = 2(x - 2)2 and y = 2 about...
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = 3/x y=0 x = 1 x = 3 Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = 1/(sq3x+5) 1 sq 3x + 5 y = 0 x = 0 x = 7
Use the disc method to find the volume generated by revolving the region bounded by y 2x2 and the lines 0 and x 2 about the x-axis. y Use the disc method to find the volume generated by revolving the region bounded by y 2x2 and the lines 0 and x 2 about the x-axis. y
1. Find the volume of the solid generated by revolving the region bounded by y = 4x - x and y = x about the x-axis. 2. Calculate the following integrals. r? a. =dx √25-x²
1) Find the volume of the solid generated by revolving the region bounded by the curves about the x-axis. Use the disk/washer method and show all work in evaluating the integral y=x", y = x 2) Find the volume of the solid generated by revolving the region bounded by the curves about the y-axis. Use the disk/washer method and show all work in evaluating the integral y=x, y = 8,x=0,
(a) Find the volume of the solid generated by revolving the region bounded by the graphs of the given equations about the x-axis. y = 0, y= x= 1, x=2 (b) Find the volume of the solid generated by revolving the region from part (a) about the line x = 3.
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...
Find the volume of the solid generated by revolving the region R bounded by the graphs of the given equations about the y-axis. 17)x= x=0, between y=- 4 and y = 4 17) 18) bounded by the circle x2 + y2 = 16, by the line x = 4, and by the line y = 4 18) Find the volume of the solid generated by revolving the region about the given line. 19) The region in the first quadrant bounded...