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 Road to Little Dribbling: More Notes from a Small Island The Road to Little Dribbling: More Notes from a Small Island The Road to Little Dribbling: More Notes From a Small Island is a humorous travel book by American author Bill Bryson, first published in 2015. Twenty years after the publication of "Notes From a Small Island", Bryson makes another journey around Great Britain to see what has changed. In the opening chapters he notes that the straight line distance from Bognor Regis on the south coast to Cape Wrath in Scotland is the longest straight line one can travel in the UK without crossing any part of the sea.