Surface area is the measure of the total area that the surface of an object occupies. In calculus, it often involves integrating to find the area of a surface generated by rotating a curve around an axis.
5 Must Know Facts For Your Next Test
The formula for surface area of revolution around the x-axis is $2\pi \int_a^b f(x) \sqrt{1+(f'(x))^2} \, dx$.
For surfaces generated by rotating around the y-axis, the formula is $2\pi \int_a^b x \sqrt{1+(f'(x))^2} \, dx$.
To calculate surface area using parametric equations, use $2\pi \int_a^b g(t) \sqrt{(f'(t))^2 + (g'(t))^2} \, dt$ for rotation around the x-axis.
Arc length must be calculated before determining surface area, as it forms part of the integrand in these formulas.
When dealing with polar coordinates, the formula for surface area involves integrating $r(\theta)$ and its derivative.