Let be continuous on

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

f

be continuous on

\mathbb R

, and let

g

be differentiable with

g(1)=0

and

g'(1)=3

. Define

F(x)=\int_{0}^{g(x)} f(t)\,dt.

Which of the following equals

F'(1)

? (a)

f\bigl(g(1)\bigr)

(b)

f(1)\,g'(1)

(c)

f\bigl(g(1)\bigr)\,g'(1)

(d)

f(1)