What is the volume of the solid produced by revolving f ( x ) = cot &#x2061;<!-- ⁡ --

DIAMMIBENVERMk1

DIAMMIBENVERMk1

Answered question

2022-06-30

What is the volume of the solid produced by revolving f ( x ) = cot x , x [ π 4 , π 2 ] around the x-axis?

Answer & Explanation

Immanuel Glenn

Immanuel Glenn

Beginner2022-07-01Added 12 answers

The formula for finding the volume of a solid produced by revolving a function f around the x-axis is
V = a b π [ f ( x ) ] 2 d x
So for f ( x ) = cot x, the volume of its solid of revolution between π / 4 and π / 2 is
V = π 4 π 2 π ( cot x ) 2 d x = π π 4 π 2 cot 2 x d x = π π 4 π 2 csc 2 x 1 d x
π [ cot x + x ] π 4 π 2 = π ( ( 0 1 ) + ( π 2 π 4 ) ) = π 1 4 π 2
gorgeousgen9487

gorgeousgen9487

Beginner2022-07-02Added 4 answers

Area of revolution around x-axis = π a b ( f ( x ) ) 2 d x
f ( x ) = cot x
f ( x ) 2 = cot x
π 4 π 2 = π 4 π 2 csc 2 x 1 d x
= π [ cot x x ] π 4 π 2
= π [ ( cot ( π 2 ) π 2 ) ( cot ( π 4 ) π 4 ) ]
= π [ ( 0 π 2 ) ( 1 π 4 ) ]
=0.674

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?