Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5 36 − x2 , y = 0, x = 2, x = 4; about the x-axis

V = 193.25π

Step-by-step explanation: The method to calculate volume of a solid of revolution is given by an integral of the form:

V =  

f(x) is the area is the function that rotated forms the solid.

For f(x)=y= and solid delimited by x = 2 and x = 4:

V =

V =

V =

V =

V = 193.25π

The volume of a solid formed by y = and delimited by x = 2 and x = 4

is 193.25π cubic units.

step-by-step explanation:

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are