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Montano1993 [528]
3 years ago
11

Find the area of the surface obtained by rotating the curve y x2 0 ≤ x ≤ 2 about the y axis

Mathematics
1 answer:
Rudiy273 years ago
4 0

<span>ds=<span>√<span>1+<span><span>(<span><span>dy</span><span>dx</span></span>)</span>2</span></span></span><span>dx</span>=<span>√<span>1+<span>14</span><span>(<span>x4</span>−2+<span>1<span>x4</span></span>)</span></span></span><span>dx</span></span>

<span>=<span>√<span><span>14</span><span>(<span>x4</span>+2+<span>1<span>x4</span></span>)</span></span></span><span>dx</span>=<span>√<span><span>1<span>22</span></span><span><span>(<span>x2</span>+<span>1<span>x2</span></span>)</span>2</span></span></span><span>dx</span></span>

<span>=<span>12</span><span>(<span>x2</span>+<span>1<span>x2</span></span>)</span><span>d<span>x</span></span></span>

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Alla [95]
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If you had meant, \frac{12}{20}, then the simplest form of this fraction would be - \frac{3}{5}

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If you had meant \frac{20}{12}, then this will certainly be of any use to you.

HOW TO UNDERSTAND THAT THE FRACTION IS IN ITS SIMPLEST FORM?
Maybe, you are just simplifying and simplifying...but you don't even know when to stop. You can understand whether a fraction is in its simplest form or not by seeing that the numerator and the denominator have a common factor to divide it by, or not.

For instance, consider the case here - \frac{3}{5} or \frac{5}{3}<span>. We can't divide it any further. So, we know that it is in its simplest form.
</span>
L O N G Process:
Well, if you want to divide it by the smallest common factor to its larger, then --
\frac{12}{20} or \frac{20}{12}

1) 
Divided by 2 = \frac{6}{10} or \frac{10}{6}

2) 
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That took much longer, right.
<span> So, it is more preferable to divide the fraction by the possible largest common factor, you can guess of.</span>

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