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Numerade Educator



Problem 58 Hard Difficulty

Find the volume of the described solid $ S $.
The base of $ S $ is the region enclosed by the parabola $ y = 1 - x^2 $ and the x-axis. Cross-sections perpendicular to the y-axis are squares.


2 units $^{3}$

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Video Transcript

recognizing what we've been getting given in the problem, Why is one mice x squared? We must write this in terms of acts as plus or minus squared of one minus y. Now that we have this, we know that we need to double this value, which means we have two times a squirt of one minus y squared. And remember, this can't be negative because we're looking at this in terms of a real world scenario, we can integrate from 0 to 1. Integrate this were literally just putting in four times one minus y of D y. Now we're gonna be using the power rule, which means we increase the experiment by one divide by the new experiment. So, for example, why the first power becomes 1/2 y squared or y squared over two. Now we're at the point where we can be plugging in. And then this is obviously just zero. When we put in zero, we get zero, which is just four times 1/2 because one minus 1/2 is 1/2. So four times 1/2 is two units cubed