This formula "defines" the integral on the left (note the dot and the vector notation for the surface element).
ð ɪ s WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY d ɪ f aɪ n z WORD_BOUNDARY ð ɪ WORD_BOUNDARY ɪ n t ɪ ɡ ɹ ə l WORD_BOUNDARY ɔ n ð ə WORD_BOUNDARY l ɛ f t WORD_BOUNDARY n oʊ t WORD_BOUNDARY ð ə WORD_BOUNDARY d ɑ t WORD_BOUNDARY æ n d WORD_BOUNDARY ð ə WORD_BOUNDARY v ɛ k t ə ɹ WORD_BOUNDARY n oʊ t eɪ ʃ ə n WORD_BOUNDARY f ə ɹ ð ə WORD_BOUNDARY s ɜː f ɪ s WORD_BOUNDARY ɛ l ɪ m ə n t WORD_BOUNDARY