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Calculus

Arc Length and Surface Area

Concept Quizzes

Arc Length by Integration
Surface Area by Integration
Arc Length and Surface Area - Problem Solving

Challenge Quizzes

Arc Length and Surface Area: Level 3 Challenges

Arc Length by Integration

If ${f}'(x) = \sqrt{ {x}^4-1 },$ what is the length of the curve $y = f(x)$ from $x = 2$ to $x = 8?$

168 164 176 172

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What is the length of the curve $y = \frac{1}{2}( {e}^x+{e}^{-x} )$ from $x = -13$ to $x = 13$ ?

\displaystyle{ {e}^{13}-\frac{1}{{e}^{13}}}

\displaystyle{ \frac{1}{{13}e}}

{13}e

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Let $L$ be the length of the line $y = 3x + 4$ on the interval $3 \leq x \leq 8$ . If $L = \sqrt{a}$ , then what is the value of $a$ ?

248 260 232 250

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Given $y \geq 0 ,$ what is the length of the curve ${y}^2 = {x}^3$ on the interval $0 \leq x \leq 4$ ?

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Let $L$ be the length of the curve $\displaystyle{y = \frac{1}{4}{x}^2 - \frac{1}{2} \ln x }$ for $4 \leq x \leq 8.$ If $L = a+\frac{1}{2}\ln{b} ,$ where $a$ and $b$ are positive integers, what is the value of $a+b?$

14 18 16 12

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