Calculus: Early Transcendentals, Chapter 6, 6.3, Section 6.3, Problem 29

int_0^3(2pix^5dx)=
2pi*int_0^3 x^5dx = 2pi*x^6 / 6|(0,3)



=pi/3 (3^6 - 0^6)= pi/3 *729 = 243pi.