ðˈʌs ðə kˈɑːnvɜːs kæn ɔːltˈɜːnətˌɪvli biː stˈeɪɾᵻd æz fˈɑːloʊz: ɪf ðɪ ˈɪntᵻɡɹəl ʌv ˌoʊvɚɹ ˈɛvɹi klˈoʊzd lˈuːp ɪnðə dəmˈeɪn ʌv ɪz zˈiəɹoʊ, ðˈɛn ɪz ðə ɡɹˈeɪdiənt ʌv sˌʌm skˈeɪlɚvˈæljuːd fˈʌŋkʃən.
Thus the converse can alternatively be stated as follows: If the integral of  over every closed loop in the domain of  is zero, then  is the gradient of some scalar-valued function.