5.12 Areas and volumes of revolution Quiz

1. $\int_0^3(x^2-3x)\,dx=-4.5$. What is the area enclosed between $y=x^2-3x$ and the $x$-axis for $0\le x\le3$?

• A. $-4.5$
• B. $4.5$
• C. $0$
• D. $9$

2. The line $y=2x$ for $0\le x\le3$ is rotated $360^\circ$ about the $x$-axis. Find the volume.

• A. $36\pi$
• B. $12\pi$
• C. $18\pi$
• D. $6\pi$

3. The region between $y=x^2$ and the $y$-axis for $0\le y\le4$ is rotated about the $y$-axis. Find the volume.

• A. $16\pi$
• B. $\frac{32\pi}{5}$
• C. $4\pi$
• D. $8\pi$

4. Why must you split the integral at points where the curve crosses the $x$-axis when finding the area?

• A. The integral is undefined at roots
• B. The curve is not continuous there
• C. Regions below the axis give negative values that cancel regions above
• D. The limits must be zero

5. The region between $y=\sqrt{x+1}$, the $x$-axis, $x=0$ and $x=3$ is rotated about the $x$-axis. Find the volume.

• A. $\frac{14\pi}{3}$
• B. $\frac{15\pi}{2}$
• C. $15\pi$
• D. $\frac{15}{2}$