Arclength & Approximating Integrals

Solution: We plot the graph for convenience. We obtain the formula:

Example 2: Solution: Simplifies to…

Unlike the last two examples, most arclength problems cannot be solved exactly because the integrals are too difficult. Example SolutionWe set up the arclength integral. This integral cannot be evaluated for an exact value, even by a computer program. We need to use an integral approximation technique

New problem SolutionWe draw a picture. Now we draw rectangles on each of the pieces. Notice, we consistently draw the rectangles so that the top-left corner lies on the graph Now we add up the total area of the rectangles (Mathematica) The correct value can be found with Mathematica’s Nintegrate function:

Facts about Numerical Integration