What is the surface area of the solid created by revolving f ( x ) = <msqrt>

Mayra Berry

Mayra Berry

Answered question

2022-06-12

What is the surface area of the solid created by revolving f ( x ) = x 3 for x [ 1 , 2 ] around the x-axis?

Answer & Explanation

Haggar72

Haggar72

Beginner2022-06-13Added 25 answers

Surface area of solid of revolution about x axis is given by the formula
S = a b 2 π y d s = a b 2 π y 1 + ( d y d x ) 2 d x. In the present case ,
d y d x = 3 2 x 1 2 , h e n c e 1 + ( d y d x ) 2 = 1 + 9 x 4
S = 2 π 1 2 x 3 2 1 + 9 x 4 d x
= π 1 2 x 3 2 9 x + 4 d x
This integration is too long to write it here. hence
use integral calculator to solve the integral
= 24.93

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