Finding the volume when the region between y = x 2 and y = 4 − x 2 is rotated about the x-axis.So I start by finding the roots where they meet, so I find: ∫ − 2 2 π ( 4 − x 2 ) 2 d xBut this got me the wrong answer 75.825. Is that right or is the book wrong with 94.7?

Question

Finding the volume when the region between   y  =      x    2   and   y  =  4  −      x    2   is rotated about the x-axis.So I start by finding the roots where they meet, so I find:      ∫          −              2                            2              π  (  4  −      x    2        )    2      d  xBut this got me the wrong answer 75.825. Is that right or is the book wrong with 94.7?

darkangel5991we · Accepted Answer

Explanation:A typical cross-section is a washer, not a disk. So we must subtract the inner radius:  V  =  π      ∫          −              2                            2              [  (  4  −      x    2        )    2    −  (      x    2        )    2    ]    d  x  =            64              2              3    π  =  94.7815  …

Chloe Arnold · Accepted Answer

Explanation:According to Mathematica you are both wrong:  ln  ⁡  4  :=      ∫          −              2                            2              π  (  4  −      x          2        )  d  x      /    n  Out     4  =  101.89You have to subtract the inner radius.

Finding the volume when the region between y=x^2 and y=4-x^2 is rotated about the x-axis.

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