Solid Leg
Given the form of a solid, determine the limits of integration necessary to create a specific volume.?
The basis of a solid is bounded by y = x ^ 2 and the line y = d. Each section of the axis perpendicular to the solid-Y is an isosceles triangle whose height is three times its base (with the short leg in the plane xy). If the volume of solid is 75, what is the value of d? Can anyone explain how develop this issue?
Between y and y + dy you a solid slap in the form of a thin (depth dy) isosceles triangle whose base from x =- sqrt (y) = x + sqrt (y) (because y = x ^ 2) (if the width is 2 sqrt (y)) and a height of three times the width. The volume of this slab is the area triangle (half the time base height) times the depth (1 / 2) (2 sqrt (y)) (3 * 2 sqrt (y)) dy y = 6. So, you want the full 6 dy yy y = 0 to D = 75 3y ^ 2 | y = low, y = top = 3D 0 d ^ 2 to 3 (0 ^ 2) = 3 d ^ 2 = 75 d ^ 2 = 25 d = 5 (can not be that y = -5 x ^ 2 is positive or zero) Dan
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