Question Number 102606 by bemath last updated on 10/Jul/20

what is the volume of region  bounded by y =x^2 −2x and  y=x that is rotated about  y=4 ?

Commented bybemath last updated on 10/Jul/20

Answered by Ar Brandon last updated on 10/Jul/20

Volume , V=π∫_0 ^3 {(x^2 −2x−4)^2 −(x−4)^2 }dx

Answered by bobhans last updated on 10/Jul/20

vol = π∫_0 ^3 (4^2 −(x^2 −2x)^2 )−(4^2 −x^2 ) dx  = π∫_0 ^3 (x^2 −(x^2 −2x)^2  dx   = π∫_0 ^3 (x^2 +x^2 −2x)(2x)dx  =4π∫_0 ^3 x(x^2 −x)dx = 4π∫_0 ^3  (x^3 −x^2 ) dx  = 4π {(1/4)x^4 −(1/3)x^3 }_0 ^3 =4π {((81)/4)−((27)/3)}   =4π {((45)/4)} = 45π

Commented byAr Brandon last updated on 10/Jul/20

What difference will it make if it was rather rotated about y=0 with respect to your solution ? 😃

Commented bybemath last updated on 10/Jul/20

😅😅😅