Let be defined by for and for

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

Let

f

be defined by

f(x)=4

for

x \leq 1

and

f(x)=2x

for

x>1

. Suppose

F

is an antiderivative of

f

such that

F(0)=3

. Determine

F(x)

for all real

x

, expressing your answer as a single piecewise function.