(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Why figure area is defined as defined integral? i have signature

[tex]P=\int\limits^b_af^{\prime}(x)\mbox{d}x=f(b)-f(a)[/tex]

what is a prove of this signature? I have other signature:

[tex]P=\lim_{n\to\infty}\sum\limits^n_1\left(x_{i+1}-x_i\right)f\left(x_i\right)[/tex]

how it can be proved that these signatures are equivalent? why cant I define figure area under [tex]f(x)[/tex] in a and b limits as ex. [tex]P=f^{\prime}(b)-f^{\prime}(a)[/tex]?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

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

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

# Homework Help: Why defined integral is figure area?

**Physics Forums | Science Articles, Homework Help, Discussion**