A student solves and writes the particular solution satisfying in two different ways:

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

Problem

A student solves

\dfrac{dy}{dx}=\ln x

and writes the particular solution satisfying

y(1)=2

in two different ways: (i)

y=2+\displaystyle\int_{1}^{x}\ln t\, dt

(ii)

y=\displaystyle\int_{0}^{x}\ln t\, dt + C

What value of

C

makes expressions (i) and (ii) equivalent for all

x>1

? (a)

1

(b)

3

(c)

2

(d)

0