# The expression for the velocity of a body is given below, where x is in meters and t is in seconds : v = dx / dt = 3t + 2 Determine the distance (x) travelled by the body in time (t) using the method of integration.

Dear Student,

$\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=3\mathrm{t}+2\phantom{\rule{0ex}{0ex}}\int \frac{\mathrm{dx}}{\mathrm{dt}}=\int 3\mathrm{t}+2\phantom{\rule{0ex}{0ex}}\mathrm{x}=\left[3\left(\frac{{\mathrm{t}}^{2}}{2}\right)+2\mathrm{t}\right]\phantom{\rule{0ex}{0ex}}\mathrm{x}=\frac{3{\mathrm{t}}^{2}}{2}+2\mathrm{t}$

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