Answer Happy

You are asked to find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x2 – x3 and y = 0. You set up your volume integral using the cylindrical shell method. 2 (circumference)(height)(thickness) 0 You write out an expression for the circumference and the height, and let thickeness = dx. When x = 1, what is the height of your cylindrical shell? (Use the expression you have written above). Answer: Check
You are asked to find the volume of the solid obtained by rotating about the x-axis the region under y = from x = 0 to x = 1. You set up your volume integral using the cylindrical shell method. x lo (circumference)(height)(thickness) 0 You write out an expression for the circumference and the height, and let thickness = dy. Your expressions for the circumference and the height are both functions of y. When y = 0, what is the height of your cylindrical shell? (Use the expression you have written above). Answer:
You are asked to find the volume of the solid obtained by rotating about the line x = 2 the region bounded by y = x - x2 and y = 0. You set up your volume integral using the cylindrical shell method. (circumference)(height)(thickness) You write out an expression for the circumference and the height, and let thickeness = dx. When x = 1, what is the radius of your cylindrical shell? (Use the expression you have written above). Answer: Check