Santhi G.
asked • 07/19/23Find the volume of the solid whose base is the region between the functions given using cross-sections of rectangles perpendicular to the x axis with a height of x
Find the volume of the solid whose base is the region between the functions given using cross sections of rectangles perpendicular to the x-axis with a height of x.
y=3(x-3)²-4
y=6-x
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2 Answers By Expert Tutors
Doug C. answered • 07/19/23
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desmos.com/calculator/tpdz65qwzx
Yefim S. answered • 07/19/23
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6 - x = 3(x - 3)2 - 4; 3x2 - 17x + 17 = 0; x = (17 ± √289 - 204)/6; x = 4.37 or x = 1.30;
V = ∫1.304.37x(6-x - 3x2 + 18x - 27 + 4)dx = ∫1.304.37(17x2 - 3x3 - 17x)dx = 41.118
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Doug C.
Wondering if there might be a typo in the problem as presented, because the points of intersection of the two functions have x-values that are irrational, making the calculation of the volume quite tedious (without a calculator)? Here is a Desmos graph to give you the idea for finding a solution for the problem as given: desmos.com/calculator/uxdfu7w4zs07/19/23