What is the surface area of the solid created by revolving f ( x ) = 2 x <m

Yasmin Camacho

Yasmin Camacho

Answered question

2022-05-20

What is the surface area of the solid created by revolving
f ( x ) = 2 x 3 2 , x [ 2 , 4 ] around the x axis?

Answer & Explanation

Samuel Vang

Samuel Vang

Beginner2022-05-21Added 12 answers

The surface area of a solid created by rotating a function f around the x axis on
x [ a , b ] is given by:
S = 2 π a b f ( x ) 1 + ( f ( x ) ) 2 d x
Here, f ( x ) = 2 x 3 2 so f ( x ) = 6 x 2 . Then:
S = 2 π 2 4 ( 2 x 3 2 ) 1 + ( 6 x 2 ) 2 d x
S = 2 π 2 4 ( 2 x 3 2 ) 1 + 36 x 4 d x
This cannot be easily integrated, so plug this into a calculator.
S=49266.1936

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