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 Sightseeing Cruises location. In 1962 it bought the famous and venerable Hudson River Day Line, keeping it as a separate brand until 1985. In 1981, the Circle Line split into two companies—Circle Line Sightseeing Cruises and Circle Line Downtown. In 1988 the 42nd Street company bought World Yacht's operating upscale dining cruises from Chelsea Piers - currently World Yacht Dining Cruises. In 1998 the 42nd Street company also launched The Beast, a speedboat ride which takes tourists around the Statue of Liberty and goes 45 mph. In 2007, the United States National Park Service said it was going to terminate Circle Line