How do you find the surface area of the solid obtained by rotating about the y-axis the region bound

britesoulusjhq

britesoulusjhq

Answered question

2022-05-11

How do you find the surface area of the solid obtained by rotating about the y-axis the region bounded by y = 1 x 2 on the interval 0 x 1?

Answer & Explanation

Julius Johnston

Julius Johnston

Beginner2022-05-12Added 17 answers

The surface area A of the solid obtained by rotating about the y-axis the region under the graph of y=f(x) from x=a to b can be found by
A = 2 π a b x 1 + [ f ( x ) ] 2 d x.
Let us now look at the posted question.
By the formula above,
A = 2 π 0 1 x 1 + 4 x 2 d x
by rewriting a bit,
= π 4 0 1 ( 1 + 4 x 2 ) 1 2 8 x d x
by General Power Rule,
= π 4 [ 3 2 ( 1 + 4 x 2 ) 3 2 ] 0 1 = π 6 ( 5 3 2 1 )

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?