A composite curve consists of two segments: • for • : the horizontal line segment…

MATHEMATICS · Single correct · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

A composite curve

\mathcal{C}

consists of two segments: •

C_{1}: x=y^{2}

for

0\le y\le 1

•

C_{2}

: the horizontal line segment from

(1,1)

(3,1)

What is the exact total length of

\mathcal{C}

? (a)

2+\sqrt{5}

(b)

\displaystyle \frac12\sqrt{5}+2

(c)

\displaystyle \frac12\sqrt{5}+\frac14\ln\bigl(2+\sqrt{5}\bigr)

(d)

\displaystyle \frac12\sqrt{5}+\frac14\ln\bigl(2+\sqrt{5}\bigr)+2