Arc length and area of a surface of revolution Quiz

1. For $y=x^2$, which expression is under the root in the arc length integral?

• A. $1+x^2$
• B. $1+2x$
• C. $1+4x^2$
• D. $1+x^4$

2. A curve is $x=2\cos t$, $y=2\sin t$. Its length for $0\leq t\leq\frac{\pi}{2}$ is

• A. $\pi$
• B. $2\pi$
• C. $2$
• D. $4\pi$

3. The polar curve $r=3$ for $0\leq\theta\leq\pi$ has length

• A. $3$
• B. $9\pi$
• C. $6\pi$
• D. $3\pi$

4. The line $y=x$ for $0\leq x\leq1$ is rotated about the $x$-axis. The surface area is

• A. $\pi$
• B. $\sqrt2\pi$
• C. $2\pi$
• D. $\frac{\pi}{\sqrt2}$

5. A curve $x=f(t)$, $y=g(t)$ is rotated about the $y$-axis. The surface area is

• A. $2\pi\int y\,ds$
• B. $\pi\int x^2\,ds$
• C. $2\pi\int x\,ds$
• D. $2\pi\int(x+y)\,ds$