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For the following exercise, find the volume generated when the region between the two curves is rotated around the given axis. Use both the shell method and the washer method. Use technology to graph the functions and draw a typical slice by hand. [T] Under the curve of y = 3x, x = 0, and x = 3 rotated around the x-axis. | Numerade
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1 - 18 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. x y = 1 , y = 0 , x = 1 , x = 2 ; about x = - 1 | Numerade
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The "washer sieve method" of integration, which finds the volume of a solid of revolution with a hole in the middle by integrating the areas of cross-sectional "washers". The method involves finding the outer and inner radii of the washers, denoted as R(x) and r(x), respectively, and using the formula V = π ∫ [R(x)² – r(x)²] dx to sum the volumes of these thin washers and find the total volume. #fbreels #ytshorts #mathskills #maths #trendingreel #trigonometry #mathschallenge #calculus #mathemati
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1-18 Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y=2-(1)/(2) x, y=0, x=1, x=2 ; about the x -axis | Numerade
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