and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the specified axis using the disk/washer method. Set up y = x2 – 1, y = 0, x = 1, x = 2, about x = 1
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- A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V=13R2H13rh2Setup, but don't evaluate, the integrals which give the volume of the solid formed by revolving the region bounded by y = x2+1, y = x, x = 1, x = 2 about these lines: a) x-axis b) y = -1 c) y = 6 d) y-axis e) x = -3 f) x = 4 g) x = 1Setup the iterated double integral that gives the volume of the following solid. Properly identify the height function h = h(x, y) and the region on the xy−plane that defines the solid.
- Setup, but don't evaluate, the integrals which give the volume of the solid formed by revolving the region bounded by y = x2+1, y = x, x = 1, x = 2 about these lines: a) x = -3 b) x = 4 c) x = 1Showing all work, use the method of your choice to find the volume of the solid obtained by rotating the region between y = x^2 and y = (2x^2) − 4 about the line x = −3. thank you!Sketch and shade the region enclosed between y=(1/2)x^2 and y=xsqrt(x). a. Rotate the region about x axis and setup an integral that gives the volume of the solid of revolution. b. Rotate the region about y axis and setup an integral that gives the volume of the solid of revolution. c. Rotate the region about y= -1 and setup an integral that gives the volume of the solid of revolution.
- setup (but do not evaluate) the integral for finding the surface area of the solid from rotating the region given byFine the volume generated by revolving the area bounded by the given curves and lines revolved about the given axis of rotation. Y = 1-x^2 y=0 is revolved about the x=1Solve by integration: A frustum of cone is made by rotating about Ox the area bounded by the lines y=x, x=0, x=a and x=b, with b>a. What is its volume?
- Question Find the volume of the solid obtained by rotating the region bounded by y=3x^2, x=1, x=3, and y=0, about the x-axis. Submit your answer in fractional form.Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. See photo. I understand that I already have the answer because the answer is already given to me but can you explain the answer. Not sure how they got there.using the shell method to find the volume of the solid obtained by rotating the region enclosed by the graphs in each part below about the y-axis a) y=x^2, y=8-x^2, and x=0 b) y=(1/2)x^2 and y=sin(x^2)