Let be a continuous function and let satisfy with the initial condition

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

Problem

Let

g

be a continuous function and let

F

satisfy

\dfrac{dF}{dx}=g(x)

with the initial condition

F(1)=3

. Which of the following expressions represents

F(x)

for all

x

in the domain of

g

? (a)

3+\displaystyle\int_{x}^{1} g(t)\,dt

(b)

\displaystyle\int_{1}^{x} g(t)\,dt

(c)

3+\displaystyle\int_{1}^{x} g(t)\,dt

(d)

3+g(x)(x-1)