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USING WASHER METHOD
Find the volume of the solid obtained by rotating about the y-axis the region bounded by y=2x2 - x3 and y = 0
DRAW GRAPH
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Solved in 2 steps with 2 images
- 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=13R2H13rh2USING DISC METHODFind the volume of the solid obtained by rotating about the y-axis the region bounded by y=2x2 - x3 and y = 0DRAW GRAPHFind the volume of the solid obtained by rotating the region bounded by y= 4 - x^2and x=0 from 0 to 2.About the y-axis. A) sketch the graph b) Find the volume.
- Find the vertex of the parabola, points of intersection, andsketch the graph of the bounded region: Find the volume of the solid generated by revolving about the line x = −2 the region bounded by the curves y = 8x − 2x2 and y = 4x − x2The base of a solid is the region bounded by the graphs of y = 4 – x2 and y = 0. The cross sections perpendicular to the y-axis are equilateral triangles. Find the volume of the solid.find the volume . The base of the solid is the region bounded by the parabola y2 = 4x and the line x = 1 in the xy-plane. Each cross-section perpendicular to the x-axis is an equilateral triangle with one edge in the plane. (The triangles all lie on the same side of the plane.)
- 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)Question Find the volume of the solid obtained by rotating the region bounded by y=3x2, x=1, x=3, and y=0, about the x-axis. Submit your answer in fractional form.Find the volume of the solid obtained by rotating the region bounded by y= x^2 —4x +5 , x=1, x=4 and the X-axis about the X-axis. A) get a sketch of the bounding region B) find the cross sectional area C) determine the limits of integration D) calculate the volume of the solid
- (a) Use cylindrical shells to find the volume of the solid that is generated when the region under the curve y = x3 −3x2 + 2x over [0, 1] is revolved about the y-axis. (b) For this problem, is the method of cylindrical shells easier or harder than the method of slicing discussed in the last section? Explain.find the volume The base of the solid is the region in the first quadrant between the line y = x and the parabola y = 2sqrt(x). The cross-sections of the solid perpendicular to the x-axis are equilateral triangles whose bases stretch from the line to the curve.region of the Cartesian plane is shaded. Use the Shell Method to find the volume of the solid of revolutionformed by revolving the region about the y-axis.