Jacob Bernoulli b. 27 Dec 1654 in Basel, Switzerland, d. 16 Aug 1705 in Basel, Switzerland, was the first to use the term integral. He studied the catenary, the curve of a suspended string. He was an early user of polar coordinates and discovered the isochrone.
Jacob Bernoulli was the brother of Johann Bernoulli and the uncle of Daniel Bernoulli. He graduated with a theology degree from Basel in 1676. He received training in mathematics and astronomy against the wishes of his parents.
Between 1676 and 1682 Jacob travelled widely in France, England and the Netherlands. He met Boyle and Hooke in England.
Jacob returned to Switzerland and taught mechanics at the University in Basel from 1683. He was appointed professor of mathematics in Basel in 1687.
Jacob was the first to use the term integral in 1690. In 1691 he studied the catenary, the curve of a suspended string.
He was an early user of polar coordinates and discovered the isochrone, the curve along which a body with uniform vertical velocity will fall.
In a mathematical dispute with his brother Johann he invented the calculus of variations. He also worked on probability theory. The Bernoulli distribution, the Bernoulli differential equation and the Bernoulli numbers are named after Jacob Bernoulli.
Jacob published many articles on infinite series
On his death his chair at Basel was filled by his brother Johann Bernoulli.