Answer to Question #116457 in Calculus for Olivia

Question

Let r(t)=0. Then ∫r(t)dt is equal to
Select one:
a. ⟨0,t,t⟩+c where c is an arbitrary constant vector

b. ⟨t,t,0⟩+c where c is an arbitrary constant vector

c. c where c is an arbitrary constant vector

d. ⟨t,t,t⟩+c where c is an arbitrary constant vector

e. ⟨t,0,t⟩+c where c is an arbitrary constant vector

f. ⟨t,0,0⟩+c where c is an arbitrary constant vector

Answer 1

the answer is (c)

Since position vector $r(t)=x(t) i+y(t)j+z(t)k$

and from the hypothesis that $r(t)=0=0 i+0j+0k$

Therefore $\int r(t)dt=\int( 0 i+0j+0k )dt$

and then

$\int r(t)dt=c_{1} i+c_{2}j+c_{3}k=c,$

where $c$ is an arbitrary constant vector