Find the volume of the solid formed by rotating the region enclosed by
$x = 0, x = 1, y = 0, y = 5 + x^{8}$
about the $x$ -axis.
$V =$
cubic units

Answer

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Answer

$\frac{4004 π}{153}$ cubic units

Steps

Step 1 ：Use the disk method to find the volume of the solid formed by rotating the region enclosed by the given equations about the x-axis.

Step 2 ：The volume of the solid is given by the integral of the area of the disks from the lower bound of x to the upper bound of x.

Step 3 ：The area of each disk is given by the formula $π r^{2}$ , where r is the distance from the x-axis to the curve $y = 5 + x^{8}$ .

Step 4 ：Set up the integral with the limits of integration from 0 to 1 and the integrand as $π (5 + x^{8})^{2}$ .

Step 5 ：Solve the integral to find the volume.

Step 6 ：The volume is $\frac{4004 π}{153}$ cubic units.

Step 7 ： $\frac{4004 π}{153}$ cubic units