Refer to the figure and find the volume generated by rotating the given region about the specified line.

$ \Re_2 $ about $ BC $

$\frac{\pi}{15}$

Applications of Integration

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in order to find the volume. You know, we have two entry along the access parallel to the axis of rotation. The Arxiv irritation is Michael's one, which means the distance from why, to the axis of rotation, Blackwell's one is gonna be our radius, which is gonna be our as one minus X to the 1/4. Because distance from the 432 extra extroverted Asian Not with complaining to the volume formula, which is pi times integral from 01 pi r squared DX. Okay, we have our bounds. Now we can plug in one minus acts to the 1/4 and then this is squared his pi r squared off. This whole thing is our This is our over here and artist Square pi r squared. Okay, now integrate. We do this by using the power which means be increased the extra in it by one. So it goes from 1/4 too 5/4 and then we divide by the new expert. We're at the point now where we can plug in our values or two bounds and we end up with pi Over 15 was our solution