Applications of Integration

The integral $\displaystyle\int_a^b f(x)dx$ can be interpreted as the sum of all tiny $f(x)dx$ values from $a$ to $b$. Here, $f(x)dx$ can be treat as product of two values: $f(x)$ and $dx$. Both carry phsical information, so the product $f(x)dx$ encapsulates the inherent physical information. Many applications of integration are based on this fundamental concept.