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

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

Short Answer

Expert verified

Differentiation and integration are inverse operations of each other.

Step by step solution

01

Step 1. Given information

It is given that vxis a function of x.

02

Step 2. Explanation

The derivative of a function vxwill be dvand integration of dvwith respect to x gives back the function vxplus 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 dvand vis that differentiation and integration are inverse operations of each other.

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