Let be continuous for all real numbers and define

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

Problem

Let

f

be continuous for all real numbers and define

g(x)=\displaystyle\int_{x}^{x^{3}} f(t)\,dt

. Derive an explicit formula for

g'(x)

in terms of

f

and

x