What is the volume of the solid produced by revolving f ( x ) = 1 x </mfrac>

Jeramiah Campos

Jeramiah Campos

Answered question

2022-06-12

What is the volume of the solid produced by revolving f ( x ) = 1 x , x [ 1 , 4 ] around the x-axis?

Answer & Explanation

Dwayne James

Dwayne James

Beginner2022-06-13Added 18 answers

Volume of revolution about the x axis is given by, V = π y 2 d x, where y is a function of x
In this case y = f [ x ] = 1 x , so V = π [ 1 x ] 2 d x.
1 x 2 can be written as x 2 , this can be integrated using the general power rule,
x n d x = x n + 1 n + 1 , g i v i n g 1 x 2 d x = 1 x
Therefore the volume will = [ π 4 ] [ π 1 ] = 3 π 4 u n i t s 3

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