What is the surface area of the solid created by revolving #f(x) = 3x, x in [2,5]# around the x axis? Calculus Applications of Definite Integrals Determining the Surface Area of a Solid of Revolution 1 Answer ali ergin May 24, 2016 #A=63sqrt10 pi# Explanation: #A=2pi int_2^5 f(x)*sqrt(1+(d f(x))/(d x))^2*d x# #f(x)=3x# #d/(d x) f(x)=3# #A=2 pi int_2^5 3x*sqrt(1+3^2)* d x# #A=2 pi int_2^5 3xsqrt 10 *d x# #A=6sqrt10 pi int_2^5 x *d x# #A=6 sqrt10[1/2 x^2]_2^5# #A=6sqrt10 pi[(1/2*5^2-1/2*2^2)]# #A=6sqrt 10 pi[25/2-4/2]# #A=6sqrt 10 pi[21/2]# #A=63sqrt10 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 499 views around the world You can reuse this answer Creative Commons License