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Numerade Educator

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Problem 60 Hard Difficulty

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

Answer

$V=2 \pi$

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Video Transcript

as specified in the problem. We know that wise to minus X squared. Now this is a pretty general formula which is V is pi Times into girl in this case are bounds are going to be from 0 to 2 as specified by the fact that problem is saying we have quarter circles, so from 0 to 2 times x squared. Do you? Why, Who the seconds of the general formula pies put out on the outside Because it's a constant access squared. OK, now plug and specifically what we know for this problem which in this case is gonna be to minus y remember that if wise to minus X square than export is two months, Why? That's why I specified in this in the beginning of the problem, which means now we could integrate using the power rule increase the expert by one divide by the new exponents. Remember, there are bounds or from zero to plugging end. We know we have two times two minus 1/2 times two square on only plug ins. Here we just get zero, which gives us two pi is equivalent to be