I’ve dropped my Calc II class because my Calc I class, which I took at the community college, never covered anti-derivatives, and my Calc II class started off assuming you already knew anti-derivatives and integration.(adsbygoogle = window.adsbygoogle || []).push({});

So now I have the fun task of teaching myself anti-derivatives and integration so I can take Calc II again next semester. So I might as well attempt the problems given as homework to the Calc II class. But unlike the homework, I’m going to choose the odd numbered problems so I can check my answers.

Q. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. [tex]

y = x^2 ,\,\,x = 1,\,\,y = 0;\,

[/tex]about the x-axis.

After drawing it, I came up with

[tex]

\begin{array}{l}

v = \sum\limits_0^1 {\pi r^2 } \Delta x = \pi \sum\limits_0^1 {r^2 } \Delta x \\

\\

v = \pi \int\limits_0^1 {r^2 ,\,dx} \\

\end{array}

[/tex]

Now here’s where my lack of anti-derivative skills hurt me. What do I do next? To get the anti-derivative of r squared, do I add 1 to the exponent and divide the whole thing by the new exponent? Should I get [tex]

\pi \frac{{r^3 }}{3}

[/tex]? If so, how do I apply this new formula to get an answer? My integral goes from 0 to 1. How do I get from here to the final answer of [tex]

\pi /5

[/tex]?

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# Homework Help: Find the volume

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