Area of a circle "ds" over the whole circle formula_33 is just the arc length, which is its circumference, so this shows that the area "A" enclosed by the circle is equal to formula_34 times the circumference of the circle. Note that the area of a semicircle of radius r can be computed by the integral formula_35. By trigonometric substitution, we substitute formula_36, hence formula_37 The last step follows since the trigonometric identity formula_42 implies that formula_43 and formula_44 have equal integrals over the interval formula_45, using integration by substitution. But on the other hand, since formula_46, the sum of the two integrals is
Circle Line Downtown Circle Line Downtown Circle Line Downtown is a sightseeing harbor cruise company that operates out of the South Street Seaport Pavilion Pier at the Financial District in Manhattan under Harbor Experience Companies. Circle Line Downtown was established by President J.B. Meyer, third generation owner and operator of the family that founded the company and Circle Line Sightseeing Cruises brand. In 1953, Frank Barry, Gerald O'Driscoll, Helen Mitchell, William Moran, and Frank Clair founded Circle Line, the nautical sightseeing operation, providing cruises which circled Manhattan. The company's fleet was then a collection of modified craft, including surplus landing crafts from World