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

Briana Petty

Briana Petty

Answered question

2022-05-29

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

Answer & Explanation

Fahrleine9m

Fahrleine9m

Beginner2022-05-30Added 11 answers

Since you are only given a single function and we are rotating about the axis of the parameter, this requires the disk method. The disk method is:
V = a b A d x
= a b π r 2 d x
= a b π [ f ( x ) ] 2 d x
We have the known values:
f ( x ) = e x
a=0
b=1
And now we can substitute:
V = 0 1 π ( e x ) 2 d x
= π 0 1 e 2 x d x
= π e 2 x 2 | 0 1
= π 2 [ e 2 e 0 ]
= π 2 [ e 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?