we have given velocity function v(t)=sint where t represent time .
we need to find distance traveled from to 1 to 5 time interval .
we need to use integration to find distance from velocity.
[tex] \int\limits^a_b {v(t)} \, dt =distance traveled [/tex].
we have a and b which is the time interval a=1 and b=5 .
[tex] \int\limits^1_5 {v(t)} \, dt=\int\limits^1_5 {sint} \, dt=-cost =(-cos(5)-(-cos(1)) [/tex]
we know that integration sint is - cost and then we need to plug the limits
distance traveled=[tex] (-0.28-(-0.54)=0.26 [/tex]
