How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region y = 16 − x 2 and 0 ≤ x ≤ 4 rotated about the x-axis?

Question

How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region   y  =  16  −      x          2       and   0  ≤  x  ≤  4 rotated about the x-axis?

bluayu0y · Accepted Answer

Explanation:The volume of a shell is surface area multiplied by thicknessThe surface area is   π      y          2      And the volume is =surface area x thickness  d  V  =  π      y          2        d  x  y  =  16  −      x          2      so       y          2        =  256  −  32      x          2        +      x          4      The volume is   V  =  π      ∫          0              4        (  256  −  32      x          2        +      x          4        )  d  x  V  =  π  (  256  −            32              x                  3                      3    +            x              5              5        )          0              4        V  =  π  (  256  ∗  4  −  32  ∗      64    3    +      1024    5    )  V  =  π  (  1024  −      2048    3    +      1024    5    )  =  546.1

How do you use the shell method to set up and evaluate the integral that gives the volume of the sol

Answered question

Answer & Explanation

New Questions in Calculus 2