For this assignment, you submit answers by question parts. The number of submiss

Question

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit on change the answer. your best submission for each question part is used for your score. Consider the curve below. y = x^3 0 lessthanorequalto x lessthanorequalto 1 Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the x-axis Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the y-axis set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve y = xe^-x, 2 lessthanorequalto x lessthanorequalto 9

Explanation / Answer

1)given y =x3,0<=x<=1

dy/dx = 3x2

ds=[1+(dy/dx)2] dx

ds=[1+(3x2)2] dx

ds=[1+9x4] dx

a) surface area about x axis =[0 to 1]2y ds

surface area about x axis =[0 to 1]2x3[1+9x4] dx

b) surface area about y axis =[0 to 1]2x ds

surface area about y axis =[0 to 1]2x[1+9x4] dx

2)

given y =xe-x,2<=x<=9

dy/dx =e-x-xe-x=(1-x)e-x

ds=[1+(dy/dx)2] dx

ds=[1+((1-x)e-x)2] dx

ds=[1+ e-2x(1-x)2] dx

a) surface area about x axis =[2 to 9]2y ds

surface area about x axis =[2 to 9]2xe-x[1+ e-2x(1-x)2] dx

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