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
A Huge Ever Growing Pulsating Brain That Rules from the Centre of the Ultraworld the sample-laden single reached #78 on the UK singles chart. A Huge Ever Growing Pulsating Brain That Rules from the Centre of the Ultraworld "A Huge Ever Growing Pulsating Brain That Rules from the Centre of the Ultraworld" is the debut single by the ambient house group The Orb. It was originally released in October 1989 and made the UK Singles Chart in 1990, peaking at #78. The 'Peel Session' version was also voted into #10 place in John Peel's 1990 Festive Fifty. In April 1991, it was released on the debut album "The Orb's Adventures Beyond the Ultraworld". The