The arc of the parabola y = x^2 from (3,9) to (4,16) is rotated about the y-axis. Find the area of the resulting surface. Please use Woframalpha only to check your final answer. Show all steps in solving the appropriate integral.

156.5

Step-by-step explanation:

Thinking process:

The area can be calculated using the formula:

We let the substitution take place.

Therefore, we let

Thus,

So,

Also, the interval of the integration changes to [ 37, 65]

Thus,

=

= 156.5 units²