Find ( oldsymbol{r}(t) ) given ( oldsymbol{r}^{prime}(t)=-t oldsymbol{i}-t oldsymbol{j}-t oldsymbol{k} ) and ( oldsymbol{r}(0)=oldsymbol{i}+2 oldsymbol{j}+3 oldsymbol{k} )
Added by Izzy S.
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Step 1
We have r'(t) = -t i - t j - t k. Now, we integrate each component with respect to t: ∫(-t) dt = -t^2/2 + C1 ∫(-t) dt = -t^2/2 + C2 ∫(-t) dt = -t^2/2 + C3 So, r(t) = (-t^2/2 + C1) i + (-t^2/2 + C2) j + (-t^2/2 + C3) k. Show more…
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