Answer:
<em>The Volume is 5.018 cubic units</em>
Explanation:
<u>Volume Of A Solid Of Revolution</u>
Let f(x) be a continuous function defined in an interval [a,b], if we take the area enclosed by f(x) between x=a, x=b and revolve it around the x-axis, we get a solid whose volume can be computed as
It's called the disk method. There are other available methods to compute the volume.
We have
And the boundaries defined as x=1, y=0 and revolved around the x-axis. The left endpoint of the integral is easily identified as x=0, because it defines the beginning of the region to revolve. So we need to compute
We need to first determine the antiderivative
Let's integrate by parts using the formula
We pick
Then
Applying by parts:
Now we solve
Making
Applying by parts again:
The last integral is directly computed
Replacing every integral computed above
Simplifying
Now we compute the definite integral as the volume
Finally
The Volume is 5.018 cubic units