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Exercises

  1. For the function $\displaystyle f(x) = \frac{\exp(-x/10)}{2+\sin(2x)}$ over the interval $-1 \leq x \leq 6$,
    A
    Plot $f(x)$ over the given interval.
    B
    Plot the approximation of the solid of revolution using LeftDisk with 12 disks.
    C
    Plot the solid formed by revolving $f(x)$ about the $x$-axis.
    D
    Find the exact volume of the solid of revolution using the RevInt command and label your output exact.
    E
    Find the number of subintervals needed to approximate the volume of the solid of revolution about the $x$-axis using LeftInt with error no greater than 0.1.

  2. Prove each of the volume formulas below by finding a function such that when revolved about the x-axis creates the solid whose volume you are trying to prove. Use the formula for the Disk method $\displaystyle \pi \int_{a}^{b} (f(x))^2 \, dx$ instead of the RevInt command.
    A
    The volume of a sphere of radius $r$ is $\displaystyle \frac{4}{3} \pi r^3$
    B
    The volume of a cylinder of radius $r$ and height $h$ is $\pi r^2h$.
    C
    The volume of a right circular cone of radius $r$ and height $h$ is $\displaystyle \frac{\pi r^2h}{3}$

  3. A maker of brass candlesticks plans to make a candlestick whose shape is given by revolving the function

    \begin{displaymath}f(x) = \frac{2}{x^2}+\frac{1}{5-x}+\frac{1}{4}\sin(\pi x) \end{displaymath}

    about the $x$ axis over the interval $0.9 \leq x \leq 4.4$. Plot the candlestick and find its volume.


next up previous
Next: About this document ... Up: lab_template Previous: Finding Volumes of Revolution
Dina J. Solitro-Rassias
2015-11-15