Sketch and shade the region bounded by the curves y=√x and y=x³,then determine the volume of the solid by revolving the region about the line y=-1. Use: Washer Method
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- A gasoline tank is an oblate spheroid generated by revolving the region bounded by the graph of x2/16 + y2/ 9 = 1 about the y-axis, where x and y are measured in feet. How much gasoline can the tank hold?Solve parts (a) and (b): Find the volume of the solid generated by revolving the region bounded by y=x^1/2 and the lines y=2 and x=0 about (a) the line y=2 and (b) the line x=4.Solve parts (a) and (b). Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y=2x+15 and the parabola y=x^2 about (a) the x-axis and (b) the line y=25.
- Use the cylindrical shells method to find the volume of the solid generated by : y = x3 , y = 1 andx = 0 and the region is revolved about y = 1 Use the cylindrical shells method to find the volume of the solid generated by : y = x3 , y = 1 and x =0 and the region is revolved about y = 1The base of a solid is the region bounded by the graphs of y = 3x,y = 6, and x = 0. The cross-sections perpendicular to the x-axisare rectangles of perimeter 20.y=x2-2x+1 and y= -x2+2x+7 Use shell method to find the volume of the solid which is obtained by rotating the region R around x=5.
- Find the volume of the solid of revolution generated when the area described is rotated about the x-axis.a.) The area between the curve y = x and the ordinates x = 0 and x =4 b.) The area between the curve y = x3/2 and the ordinates x = 1 and x = 3 c.) The area between the curve x2 + y2 + 16 and the ordinates x = -1 and x = 1a) On a set of coordinate axes, sketch the region in Q1 that is bounded by the graphs of equations y=0, x=3, and y=(1/10)x^4. Give the coordinates of the three "corners" of this region. b) Use the Washers method to find the volume of the solid created in revolving the region from part a) about the y-axis.Graphs of x=f(y)=y(11−2y) and x=0 enclose a region in the first quadrant. Rotating that region about the x-axis generates a solid whose volume is:
- Graph and shade the region enclosed by the curves y = 2 - x^2and y = x2 . Determine the volume of the solid obtained by rotating the shaded region about the line (a) y =-1 and (b) x =-1the region bounded by the graph y = 3x - x3, the y axis, and the line y = 2 is revolved about y axis. The solid of revolution is ______ . A. Disk B. WasherC. Cylindrical Shell D. PyramidFind the centroid of the given region. [Give exact answer in fraction form.] y=2-x2, y=x