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Chapter 11: Q. 19 (page 872)

Whatistherelationshipbetweenthegraphofadifferentiablevectorfunctionr(t)andthegraphof鈭�r'(t)dt,oneoftheantiderivativesofr'(t)?

Short Answer

Expert verified

Thegraphofr(t)andr'(t)differbyaconstantvector.

Step by step solution

01

Step 1. Given information is:

Adifferentiablevectorfunctionr(t)

02

Step 2. Integrability of y=f(x) on [a,b]

Letf:[a,b]鈫�R.LetfhasanantiderivativesfonI.ThenwesaythatfhasanintegralfonIandforanyrealconstantc,wesayF+canindefiniteintegraloffover[a,b]denotedby鈭�f(x)dx.Thus,鈭�f=鈭�f(x)dx=F(x)+cThesamethingappliestovectorfunctionalso.So,鈭�r'(t)dt=r(t)+c,wherecisaconstantvector.Thus,thegraphofr(t)andr'(t)differbyaconstantvector.

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