Question

Find the volume of the solid that is obtained by revolving

the region bounded by the graph of y=x-x^2 and the x-axis about the x-axis.
Round your answer to four digits after the decimal sign

Answer 1

volume is 0.1047 cubic units

Explanation:

x goes from 0 to 1 here because of the x intercepts

f(x) = x - xx

f(x) = x*(1-x)
revolving around the x-axis

Volume = integral [3.1415* [f(x)]^2 ] dx from 0 to 1

f(x)^2 = x*x *(1-x)*(1-x)

f(x)^2 = xx ( 1-2x +xx)

f(x)^2 = xx -2xxx + xxxx

Integration...

(1/3)xxx - (1/2)xxxx + (1/5)xxxxx

Volume = 3.1415 * (1/3 -1/2 +1/5)

V = 3.1415* (8/15 -1/2)

V = 3.1415/30

V = 0.1047 cubic units

From MysticAlanCheng