Let be the curve defined by for

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

Problem

Let

C

be the curve defined by

x=y^{2}+1

for

0\le y\le 3

. Determine the exact length of

C

. (a)

\displaystyle \frac{3}{2}\sqrt{37}

(b)

\displaystyle \frac{3}{2}\sqrt{37}+\frac14\ln\bigl(3+\sqrt{37}\bigr)

(c)

\displaystyle \frac{3}{2}\sqrt{37}+\frac14\ln\bigl(6+\sqrt{37}\bigr)

(d)

\displaystyle \frac{3}{2}\sqrt{37}+\frac12\ln\bigl(6+\sqrt{37}\bigr)