Answer:
156.5
Step-by-step explanation:
Thinking process:
The area can be calculated using the formula:
[tex]S = \int\limits^4_3 {2\pi x\sqrt{1+}(2x)^{2} } \, dx[/tex]
We let the substitution take place.
Therefore, we let [tex]u = 1 + 4x^{2}[/tex]
Thus, [tex]du = 8dx.[/tex]
So,
[tex]xdx = \frac{1}{8}du[/tex]
Also, the interval of the integration changes to [ 37, 65]
Thus,
[tex]S = \int\limits^4_3 {2\pi \sqrt{1+4x^{2} } } \, dx \\= \int\limits^65_35 {2\pi \sqrt{\frac{1}{8}u } } \, dx[/tex]
= [tex]\frac{1}{6} [ 65^{\frac{3}{2}-37^{\frac{3}{2} } }[/tex]
= 156.5 units²
