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 integral.)
Find the volume of the solid obtained by revolving the region bounded by the graphs of the functions 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
(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 generated by revolving the plane region bounded by the graphs of the functions: y = et, y = 0,x = 0, and x = 4 about the x -axis.
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.
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
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...
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. 1 y = 8x + y = 0 X=0 X = 9
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 5. Need Help? Read Watch Water Takto Tutor Submit Answer Practice Another Version -/1 points LarCalc 10 7.2.017. My Notes Ask Your Teacher Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 3. (Round your answer to three decimal places.) Need Help? Read...
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