Find the area of the surface generated by revolving about the x-axis the portion of the astroid x Superscript two thirds Baseline plus y Superscript two thirds Baseline equals 9 Superscript two thirds equal to one x(3/2)+y(2/3)=1)

The correct question is:

Find the area of the surface generated by revolving about the x-axis, the portion of the astroid

The Surface Area is

Step-by-step explanation:

First, we rewrite the expression in terms of x,  because we are revolving about the x-axis, we want to integrate in terms of x. Doing that, we have

Next, we differentiate y with respect to x

Thus,

and so

Therefore, the Surface Area is given as:

If we let

then

so we see that

x

step-by-step explanation: