ðə ɡɹˈeɪdiənt θˈiəɹəm, ˈɔːlsoʊ nˈoʊn æz ðə fˌʌndəmˈɛntəl θˈiəɹəm ʌv kˈælkjʊləs fɔːɹ lˈaɪn ˈɪntᵻɡɹəlz, sˈɛz ðˌæɾə lˈaɪn ˈɪntᵻɡɹəl θɹuː ɐ ɡɹˈeɪdiənt fˈiːld kæn biː ɪvˈæljuːˌeɪɾᵻd baɪ ɪvˈæljuːˌeɪɾɪŋ ðɪ ɚɹˈɪdʒɪnəl skˈeɪlɚ fˈiːld æt ðɪ ɛndpˈɔɪnts ʌvðə kˈɜːv.
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve.