Day 189 · Jul 7

Birthday of Maria Gaetana Agnesi (1718)

Maria Agnesi wrote the first surviving mathematical work by a woman: ‘Analytical Institutions for the Use of Italian Youth’ (1748), a comprehensive two‑volume calculus textbook. She included the curve y = a³/(a² + x²) – the ‘witch of Agnesi’ (from a mistranslation of the Italian ‘versiera’, meaning ‘versed sine curve’). Pope Benedict XIV appointed her professor at the University of Bologna, though she never taught, later devoting her life to charity. She spoke seven languages and was a child prodigy in mathematics and philosophy.

The witch of Agnesi has a peak at (0, a) and approaches 0 as x → ±∞. What is the area between the curve and the x‑axis? (Hint: it’s a simple multiple of a².)

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