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
There Is a Light That Never Goes Out There Is a Light That Never Goes Out "There Is a Light That Never Goes Out" is a song by the English rock band the Smiths, written by guitarist Johnny Marr and singer Morrissey. Featured on the band's third studio album "The Queen Is Dead", it was not released as a single in the United Kingdom until 1992, five years after their split. It peaked at No. 25 on the UK Singles Chart. The song has received considerable critical acclaim; in 2014, "NME" listed "There Is a Light That Never Goes Out" as the 12th greatest song of all time.