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 the band's "comeback" record. However, Johnny Marr was insistent that "Bigmouth Strikes Again" be the band's next single. Despite Travis's advocation of the song, Simon Goddard expressed doubt that the song's "explicit glamorisation of suicide" would have endeared it to daytime radio. Regardless, "There Is a Light That Never Goes Out" became the second Smiths song to top BBC Radio One disc jockey John Peel's Festive Fifty poll in his 1986 tally. The song was shortly thereafter included on the 1987 compilation album "The World Won't Listen". In October 1992, "There Is a Light That Never Goes Out" finally received