\magnification=\magstep1


$$
\int{ 5 t \thinspace dt} \quad =? \quad 5 t^2
$$

$$
{{d}\over{dt}}{( 5 t^2 )} \quad = \quad 10t 
$$

$$
\int{ t^N \thinspace dt } \quad = \quad {({{1}\over{N+1}})} \thinspace t^{N+1}
$$

$$
\int{ 56.8 t^3 \thinspace dt } \quad = \quad ?? 
$$


$$
\eqalign{
\int{ 56.8 t^3 \thinspace dt } \quad &= \quad 56.8 \int{ t^3 \thinspace dt } \cr
                                    &= \quad 56.8  \thinspace
               \left ( {{1}\over{4}} t^4 \right ) \cr
                                    &= \quad 14.2 t^4  \cr
}
$$

$$
(x - x_0) \quad = \quad \int{ 35 {\rm\ m/s\ } \thinspace dt }
$$

$$
{\rm mass\ } \quad = \quad \int{ \rho(V)  \thinspace dV }
$$

$$
v(t) \quad = \quad 30 ({\rm m/s}) - 2 ({\rm m/s^2 }) t
$$

$$
\eqalign{
(x - x_0) \quad &= \quad \int_{t=0 {\rm s}}^{t=2{\rm s}} { v(t) \thinspace dt } \cr
 \cr
          &= \quad \int_{t=0 {\rm s}}^{t=2{\rm s}} 
             { \Bigl ( 30 ({\rm  m/s }) - 2 ({\rm  m/s^2 }) t \Bigr ) 
                       {  \thinspace dt } } \cr
 \cr
          &= \quad \Bigl (
              30 ({\rm  m/s }) t -  1 ({\rm  m/s^2 }) t^2 
                   \Bigr ]_{t=0{\rm s}}^{t=2{\rm s}} \cr
}
$$

$$
(x - x_0) \quad = \quad \left [ 30 ({\rm m/s}) (2 s) - 1 ({\rm  m/s^2 }) (2 s)^2 \right ]
                 -
            \left [ 30 ({\rm m/s }) (0 s) - 1 ({\rm  m/s^2 }) (0 s)^2 \right ]
$$



\bye

