∫ 5t dt =? 5t^{2}

\frac{d}{dt}(5t^{2}) = 10t

∫ t^{N} dt = (\frac{1}{N + 1}) t^{N+1}

∫ 56.8t^{3} dt = ??

∫ 56.8t^{3} dt = 56.8 ∫ t^{3} dt

= 56.8 (\frac{1}{4}t^{4})

= 14.2t^{4}

(x − x_{0}) = ∫ 35 m/s dt

mass = ∫ ρ(V) dV

v(t) = 30(m/s) − 2(m/s^{2})t

(x − x_{0}) = ∫_{t=0s}^{t=2s} v(t) dt

= ∫_{t=0s}^{t=2s} (30(m/s) − 2(m/s^{2})t) dt

= (30(m/s)t − 1(m/s^{2})t^{2}]_{t=0s}^{t=2s}

(x − x_{0}) = [30(m/s)(2s) − 1(m/s^{2})(2s)^{2}] − [30(m/s)(0s) − 1(m/s^{2})(0s)^{2}]