8 - Definite Integrals (1) (Properties Theory And Geometrical Meaning)

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In this video we learn that Integration stands for Continuous Summation.
We also clear a common misconception among students that Integration always gives Area.
Finally we learn the properties of Definite integrals with a logical approach.

$\color{red}{\text{For Quick Reference I have Kept the Properties Here}}$
$\color{blue}{\int ^{a}_{a}f\left( x\right) dx=0}$

$\int ^{b}_{a}f( x) dx=-\int ^{a}_{b}f( x) dx$

$\int ^{b}_{a}f\left( x\right) dx=\int ^{c}_{a}f\left( x\right) dx+\int ^{b}_{c}f\left( x\right) dx,~a<c<b$

$\int ^{a}_{0}f\left( x\right) dx=\int ^{a}_{0}f\left( a-x\right) dx$

$\int ^{a}_{-a}f\left( x\right) dx=\begin{cases}0,if~f\left( x\right) is~ odd\\ 2\int ^{a}_{0}f\left( x\right) dx,if~f\left( x\right) is~ even\end{cases}$