What is the surface area of the solid created by revolving #f(x)=2-x# over #x in [2,3]# around the x-axis? Calculus Applications of Definite Integrals Determining the Surface Area of a Solid of Revolution 1 Answer ali ergin Apr 17, 2016 #A=-sqrt2 pi# Explanation: #A=2piint_2^3 f(x)sqrt(1+(d/(d x) f(x))^2 )d x# #d/(d x)f(x)=-1# #(d/(d x)f(x))^2=1# #A=2pi int_2^3 (2-x)sqrt(1+1)d x# #A=2 pi int _2^3 (2-x)sqrt2* d x# #A=2sqrt2 pi int_2^3 (2-x)d x# #A=2 sqrt2 pi|2x-x^2/2|_2^3# #A=2 sqrt2 pi[(2*3-3^2/2)-(2*2-2^2/2)]# #A=2 sqrt2 pi[(6-9/2)-(4-2)]# #A=2sqrt2 pi[3/2-2]# #A=2sqrt2 pi(-1/2)# #A=-sqrt2 pi# Answer link Related questions How do you find the surface area of a solid of revolution? How do you find the surface area of the solid obtained by rotating about the #y#-axis the region... How do you find the surface area of the solid obtained by rotating about the #x#-axis the region... How do you find the surface area of the solid obtained by rotating about the #x#-axis the region... How do you find the surface area of the solid obtained by rotating about the #y#-axis the region... How do you find the surface area of the solid obtained by rotating about the #x#-axis the region... How do you find the surface area of the solid obtained by rotating about the #x#-axis the region... How do you find the surface area of the part of the circular paraboloid #z=x^2+y^2# that lies... How do you determine the surface area of a solid revolved about the x-axis? How do you find the centroid of the quarter circle of radius 1 with center at the origin lying... See all questions in Determining the Surface Area of a Solid of Revolution Impact of this question 377 views around the world You can reuse this answer Creative Commons License