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Cylinders Let S be the solid in
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- find the volume The solid lies between planes perpendicular to the x-axis at x = 0 and x = 4. The cross-sections perpendicular to the axis on the interval 0<=x<= 4 are squares whose diagonals run from the parabola y = -sqrt(x) to the parabola y = sqrt(x).arrow_forwardfind 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.)arrow_forwardConsider solid obtained that the region bounded by the lines x = 0, x = 6 - y , and y = 3. Sketch the region and sketch a slice that is perpendicularto the y-axis. Find the area function of the slices A ( y ). Integrate A ( y ) to determine the volume of the solid.arrow_forward
- volume of the solid generated when the region bounded by y = 9 − x2 and y = 2x + 6 is revolved about the x-axis.arrow_forwardR is the region bounded by y= sqrt x , and y= 6-x and the vertical y-axis. Q is the region bounded by y= sqrt x, and y=6-x, and the horizontal x- axis. (They Intersect at (4,2) ) Write an expression that gives the volume of the solid formed by rotating R around the horizontal line y=-2arrow_forward
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