(13) What is the volume of the solid obtained by revolving the function x H(x) =...
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 volume of the solid formed by revolving bounded by the
first figure. and the x-axis around the x-axis.
8 y = x2 + 4 and the x-axis around the x-axis y
Please solve #13 and #17.
In Exercises 13-16, use the shell method to set up and evaluate the integral that gives the volume of the solid generated hy revolving the plane region about the x-axis. 14.,-2-х 13.) у х 12 -2十 In Exercises 17-20, use the shell method to find the volume of the solid generated by revolving the plane region about the indicated line. x2, y 4x x2, about the linex-4 y
In Exercises 13-16, use the shell method...
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...
3. Find the volume of the solid obtained by revolving the region below y = 4 – 22 and above y=0, for –25252, about the z-axis. [10] 4. a. Find the arc-length of the curve y = ln (cos(x)), where 0 SES [6] b. Find the average value of tan(x) on the interval [0, 1]. [4] 7T
Find the volume of the solid obtained by revolving the indicated region about the given line. (Tip: Making a rough sketch of the region that’s being rotated is often useful.). The region is bounded by the curves x = √ sin y, x = 0, y = 0, and y = π and is rotated about the y -axis.
18. Evaluate: dx 19. Evaluate: dv 20. Find the volume of solid generated by revolving the region bounded by gra e,y-0, and x -0 about the x-axis.
18. Evaluate: dx 19. Evaluate: dv 20. Find the volume of solid generated by revolving the region bounded by gra e,y-0, and x -0 about the x-axis.
30 points) (a) (12 points) Set up an integral representing the volume of the solid obtained by rotating about the x-axis the region bounded by y = x3 + 1, x = 0, x = 2, and y= 1. You do not need to evaluate the integral. (b) (18 points) Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x – x2 and y= 0.
27) In order to find the volume of the solid of revolution created by revolving the area under the curve y= x(over the interval [-1,3]) around the x-axis: Sketch the region, Draw the Representative disk or washer, Label i, Label the thickness, and Label the radius with the appropriate function. Write the Riemann Sum
27) In order to find the volume of the solid of revolution created by revolving the area under the curve y= x(over the interval [-1,3]) around...
(b) Use the Shell method to compute the volume of the solid obtained by revolving the region bounded by the graphs of 1g(r) = 3 - r f(x) about the line x = 2
(b) Use the Shell method to compute the volume of the solid obtained by revolving the region bounded by the graphs of 1g(r) = 3 - r f(x) about the line x = 2