What is the surface area produced by rotating f ( x ) = x <mrow class="MJX-TeX

Winigefx

Winigefx

Answered question

2022-06-22

What is the surface area produced by rotating f ( x ) = x 3 8 , x [ 0 , 2 ] around the x-axis?

Answer & Explanation

Kaydence Washington

Kaydence Washington

Beginner2022-06-23Added 32 answers

first find dS, note the radius of the rotation is x.
d S = 1 + 9 x 4 d x
0 2 2 π x d S
to solve make a substitution of w = 3 x 2
Explanation:
If you make the substitution with w your integral becomes
0 12 π 3 1 + w 2 d w
with a trigonometric substitution w = tan ( θ )
the integral becomes
π 3 0 arctan ( 12 ) sec 3 ( θ ) d ( θ )
which you can solve by parts or using a table.

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