I learned in my calc 1 class that to calculate the arc length of a curve, we are to compute the integral of the function. For example, the integral of a function that describes the path of a thrown baseball would give the total distance traveled by the baseball (I hope i'm using the term arc length correctly to describe this).(adsbygoogle = window.adsbygoogle || []).push({});

However, we also learned that finding the integral of a function gives you the area under the curve described by the function. I must have a fundamental misunderstanding of either one or both of these statements, because if they are accurate, then what happens when you take the integral of a semi-circle? Then multiply it by 2? Something doesn't work out because I know the length of the curve (circumference of a circle, C=2pi(r)) is different than the area under/in-between the curves (A=pi(r)^2).

I would greatly appreciate if someone could please help me understand this apparent paradox.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integral area and arc length

Loading...

Similar Threads - Integral area length | Date |
---|---|

I Q about finding area with double/volume with triple integral | Sep 13, 2017 |

Question about area between curves (integral calc textbook q | Aug 4, 2017 |

I Area of sector by integration | Mar 5, 2016 |

How to work out the area of an elliptical wing? | Feb 16, 2016 |

Polar integration - Length and Area of curve | Nov 4, 2013 |

**Physics Forums - The Fusion of Science and Community**