🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning Oh no! Our educators are currently working hard solving this question. In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics. Numerade Educator ### Problem 46 Easy Difficulty # (a) A model for the shape of a bird's egg is obtained byrotating about the$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,$a=-0.06, b=0.04c=0.1,$and$d=0.54 .$Graph$f\$ and find the volumeof an egg of this bird.

#### Topics

Applications of Integration

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

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### Video Transcript

{'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"}

#### Topics

Applications of Integration

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp