arc length, y axis

[bcddd214]

y=?x+2
[1,2]
y=x^(1/3)+2
rotating on the y axis.

I get right here in the beginning and freeze pondering (should I be solving for y first or does y axis simply mean solve for x and not the equation?).

 

[bcddd214]

y=?x+2
[1,2]
y=x^(1/3)+2
rotating on the y axis.

I get right here in the beginning and freeze pondering (should I be solving for y first or does y axis simply mean solve for x and not the equation?).

referring to y=function or x=distance from origin...

 

[galactus]

Is it arc length or a solid of revolution?. How are we rotating if its arc length?.

What is the exact problem statement?.

 

[bcddd214]

I apologize. here is the question.

In Exercises 27, find the area of the surface of
revolution generated by revolving the given plane curve
over the indicated interval about the y-axis.

 

[galactus]

Oh, it's neither arc length nor a solid...it's a surface of revolution.

Since it is being revolved about the y axis, express in terms of y. Change the limits of integration accordingly.

Solve \(\displaystyle x^{\frac{1}{3}}+2=y\) for x in terms of y.

\(\displaystyle g(y)=(y-2)^{3}\)

Use the surface of revolution formula. \(\displaystyle 2\pi\int_{a}^{b}g(y)\sqrt{1+[f'(y)]^{2}}dy\)