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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

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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