Generalized FTC with variable limits for JEE

Formula

\[\frac{d}{dx}\left(\int_{\phi(x)}^{\psi(x)} f(t)\,dt\right)=f(\psi(x))\psi'(x)-f(\phi(x))\phi'(x)\]

Variables: \(\phi(x),\psi(x)\) are differentiable limit functions.

Conditions: \(f\) continuous on relevant interval.

Differentiation under variable limits.