If the two lines and intersect at a point

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

Problem

If the two lines

AB:\left(\displaystyle\int_0^{2t}\left(\dfrac{\sin x}{x}+1\right)dx\right)x+y=3t

and

AC:2tx+y=0

intersect at a point

A

, then the

x

-coordinate of

A

t\to0

\dfrac pq

, where

p

and

q

are in lowest terms. Find

p+q