$[5/9$ Points$]$

This question has several parts that must be completed sequentially. If you skip a part

Tutorial Exercise

Find $r(t)$ if $r^{\text{'}}(t)=9t^{8}i10t^{9}j\sqrt[\phantom{2}]{t}k$ and $r(1)=ij.$

Step $1$

Recall that integrals of vector functions are obtained by integrating each compone

$r^{\text{'}}(t)=9t^{8}i10t^{9}j\sqrt[\phantom{2}]{t}k$

$r(t)=({\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}9t^{8}dt)i({\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}10t^{9}dt)j({\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{t}dt)k$