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AP® Calculus AB-BC

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Difficult

Length of Curve Between Points

APCALC-BNL1IB

Determine which expression could represent the length of the curve $y = x^2 – 1$ from the point $(-1, 0)$ to $(3, 8)$.

$I.\ \int _{ -1 }^{ 3 }{ \sqrt { 1+4{ x }^{ 2 } } dx } $

$II.\ \int _{ 0 }^{ 8 }{ \sqrt { 1+\cfrac { 1 }{ 4y+4 } } } dy$

$III.\ \int _{ -1 }^{ 3 }{ \sqrt { 1+2x } dx } $

A

I only

B

II only

C

I and III

D

I and II