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Problem 46 Easy Difficulty

(a) A model for the shape of a bird's egg is obtained by
rotating about the $x$ -axis the region under the graph of
$$
f(x)=\left(a x^{3}+b x^{2}+c x+d\right) \sqrt{1-x^{2}}
$$
Use a CAS to find the volume of such an egg.
(b) For a Red-throated Loon, $a=-0.06, b=0.04$
$c=0.1,$ and $d=0.54 .$ Graph $f$ and find the volume
of an egg of this bird.

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{'transcript': "Okay, We know that via fax can be written as pie times The integral from negative 1 to 1 of X cubed was B X squared asiax pastilles, times square root of one minus X squared DX, which means we're integrating from negative 1 to 1. Therefore, we know we can also write this using C A s as pi times for a squared over 63. A c over 35 us for B squared over 35 was a P D over 15. Now, looking at part B, we already know what we have for part A. Therefore, we can simply substitute given values for A, B, C and D. And then if you want a graphical visual, you have this. Which means you can also said you can use a graphical visual as well to figure out via axe. If this is easier for you can put this into a formula like into a program like gizmos, for example, and you should get 1.263 or you can plug in directly A, B, C and D"}

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