13. Let a 0. (a) [2 marks] For this part of the question only, select a...

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13. Let a 0. (a) [2 marks] For this part of the question only, select a specific a > 0, and draw a large sketch of the curve y=x" on the domain [0, 1] below, indicating your particular choice of a clearly. y (b) [4 marks] Let A be the area under the curve y = 2" from x = 0 to z = 1. Find, as a function of a, the volume of the solid obtained by rotating A about the x-axis. 5 (c) [4 marks] Again, let A be the area under the curve y = 2 from x = 0 to x = 1. Find, as a function of a, the volume of the solid obtained by rotating A about the y-axis. (d) [3 marks] Find the constant a 0 such that the solids described in parts (b) and (c) have the same volume. Explain, without using calculus, why that choice of constant yields two shapes of the same volume. 13. Let a 0. (a) [2 marks] For this part of the question only, select a specific a > 0, and draw a large sketch of the curve y=x" on the domain [0, 1] below, indicating your particular choice of a clearly. y (b) [4 marks] Let A be the area under the curve y = 2" from x = 0 to z = 1. Find, as a function of a, the volume of the solid obtained by rotating A about the x-axis. 5 (c) [4 marks] Again, let A be the area under the curve y = 2 from x = 0 to x = 1. Find, as a function of a, the volume of the solid obtained by rotating A about the y-axis. (d) [3 marks] Find the constant a 0 such that the solids described in parts (b) and (c) have the same volume. Explain, without using calculus, why that choice of constant yields two shapes of the same volume.