Find a vector valued function satisfying given properties

by RoRi

June 1, 2016

If $A$ and $B$ are fixed vectors and $F$ is a vector valued function with

$F''(t) = tA + B,$

find $F(t)$ if $F(0) = D$ and $F'(0) = C$ .

We have

$\begin{align*} && F''(t) &= tA + B \\ \implies && \int F''(t) \,dt &= \int (tA+B) \, dt \\ \implies && F'(t) &= \frac{1}{2}t^2 A + tB + C \\ \implies && F(t) &= \frac{1}{6} t^3 A + \frac{1}{2}t^2 B + tC + D. \end{align*}$

Stumbling Robot

Find a vector valued function satisfying given properties

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