Question

Suppose v(x) is a function of x. Explain why the integral

of dv is equal to v (up to a constant).

Short answer

Differentiation and integration are inverse operations of each other.

Step-by-step solution

Step 1. Given information

It is given that $v\left(x\right)$is a function of x.

Step 2. Explanation

The derivative of a function $v\left(x\right)$will be $dv$and integration of $dv$with respect to x gives back the function $v\left(x\right)$plus a constant because the integration of a derivative with respect to the same variable results in the function itself. So, the reason of equality of $\int dv$and $v$is that differentiation and integration are inverse operations of each other.