A curve consists of two pieces

MATHEMATICS · Subjective · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

A curve consists of two pieces. For

0 \le x \le 1

, the curve is the graph of

y = x^{2}

. For

1 \le x \le 3

, the curve is the graph of

y = mx + b

. The curve is required to be continuous and to have a continuous derivative at

x = 1

. Determine the values of

m

and

b

, and then determine the total length of the curve on

0 \le x \le 3