Question

Evaluate \[\frac{d}{dx}\left(\int f(x)\,dx\right).\]

Options

• \[f(x)+C\]

• \[f(x)\]

• \[\int f(x)\,dx\]

• \[f'(x)\]

Answer 1

Differentiation of an indefinite integral returns the integrand. Hence, \[\frac{d}{dx}\left(\int f(x)\,dx\right)=f(x).\] This expresses that differentiation and indefinite integration are inverse processes.