Determine whether the following statements are true and give an explanation or counterexample. If f is not one-to-one on the interval [a, b], then the are of the surface generated when the graph of f on [a, b] is revolved about the x-axis is not defined.

Step-by-step explanation:

The missing equation is:

Suppose f = nonnegative function whose first derivative is within (a,b) and it is continuous, Then the area of the surface generated is revolved about the x-axis:

The area of the surface revolution is:

So; if   for

Then; substituting a with c and b with d; f(x) also with g(y) and dx with dy;

Then;

SInce;

; Then the statement is false.

Provided that the semicircle isn't on interval.

Then, the solid generated by the revolution about the x-axis is a sphere.

However, the surface is well defined and the statement is false.