Let be continuous on an interval and let and be differentiable on that interval

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

f

be continuous on an interval and let

u(x)

and

v(x)

be differentiable on that interval. State an explicit formula for

\frac{d}{dx}\int_{u(x)}^{v(x)} f(t)\,dt

in terms of

f,\,u,\,v,

and their derivatives.