Question

How do you use the first fundamental theorem of calculus$?$

Answer 1

First fundamental theorem of calculus:

The first fundamental theorem of calculus is also called the first part of the fundamental theorem of calculus and it states that the function $f$ is continuous in the closed interval $[a,b]$ and $F$ is the indefinite integral of a function $f$ on $[a,b]$ such that:

$\mathit{F}\mathbf{\left(}\mathit{b}\mathbf{\right)}\mathbf{}\mathbf{-}\mathbf{}\mathit{F}\mathbf{\left(}\mathit{a}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{\int }}_{\mathbf{a}}^{\mathbf{b}}\mathbf{}\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{}\mathit{d}\mathit{x}$

This is used to find the area of a region under the curve $y=f\left(x\right)$between $x=a$ and $x=b$.

Hence, the first fundamental theorem of calculus is used to find the area under the curve.