Posted by Anonymous on .
The velocity function is v(t) = t^2  6 t + 8 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [1,6].

math 
Anonymous,
v=ds/dt
ds/dt=t^26t+8
ds=(t^26t+8)*dt
s=integral(t^26t+8)*dt
s=(t^39t^2+24t)/3+C
s=(t/3)*(t^29t+24)+C
s=(t/3)*[(t9)*t+24)]+C
s=Definite integral betwen(1,6)
s=(6/3)*[(69)*6+24](1/3)*[(19)*(1)+24]
s=(6/3)*[(3)*6+24]+(1/3)*[10*(1)+24]
s=2*(18+24)+(1/3)*(10+24)
s=2*6+(1/3)*34
s=12+34/3
s=(36/3)+(34/3)
s=70/3