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
The Penguin Goes Straight The Penguin Goes Straight The Penguin Goes Straight is the 21st episode of the "Batman" television series, first airing on ABC March 23, 1966. It guest starred Burgess Meredith as The Penguin. Attending a matinee performance at a Gotham City theatre, the Penguin foils a thief’s attempts to steal a ruby from the beautiful actress Sophia Starr. Then, at the Millionaire's Club, he stops two crooks from kidnapping millionaire Reggie Rich from a steam room. When Batman and Robin arrive, the Penguin announces his Penguin Protection Agency, which will protect the wealth of Gotham City's society crowd. Batman and Robin