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# (a) A model for the shape of the bird's egg is obtained by rotating about the x-axis the region under the graph of $$f(x) = (ax^3 + bx^2 + cx + d) \sqrt{1 - x^2}$$Use $CAS$ 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 species.

## a) $V(x)=\pi\left[\frac{4 a^{2}}{63}+\frac{8 a c}{35}+\frac{4 b^{2}}{35}+\frac{8 b d}{15}+\frac{4 c^{2}}{15}+\frac{4 d^{2}}{3}\right]$b) $V(x) \approx 1.263$

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