- Calculate the length of a curve described by y=f(x) from one point to another
- Find the length of a curve defined by x=g(y) from one point to another
- Calculate the total surface area of a solid formed by rotating a curve around an axis
Calculating Arc Lengths and Surface Area in Various Scenarios
In this apply-it task, we’ll explore how to calculate the arc lengths of different curves as well as surface area. We’ll work with functions expressed in terms of [latex]x[/latex] and [latex]y[/latex], applying the formulas we’ve learned to determine the length of curve segments. Remember, the key to solving these problems is setting up the correct integral based on how the function is expressed and the given interval.