Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves?

Oh, shells might be easiest. Y = x² and y =?x. Each shell has radius r = x - -1 = x + 1 and height h =?

X - x². Then V =? A,b 2?

Rh dx = 2?0,1 (x + 1)(?x - x²) dx = 2?0,1 (x^(3/2) - x³ +? X - x²) dx V = 2?((2/5)x^(5/2) - (1/4)x^4 + (2/3)x^(3/2) - x³/3) |0,1 V = 2?(2/5 - 1/4 + 2/3 - 1/3 - (0)) = (2? /60)(24 - 15 + 40 - 20) = (?/30)(29) = 29?

/30 By washers, we've got x =? Y and x = y² Each washer has outer radius R = x1 - -1 =? Y + 1?

R² = y + 2? Y + 1 and inner radius r = x2 - -1 = y² + 1? R² = y^4 + 2y² + 1 Then V =?

A,b?(R² - r²) dy =?0,1 (y + 2? Y - y^4 - 2y²) dy V =?(y²/2 + (4/3)y^(3/2) - (1/5)y^5 - (2/3)y³) |0,1 V =?(½ + 4/3 - 1/5 - 2/3 - (0)) = (?/30)(15 + 40 - 6 - 20) = 29? /30.

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