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 home") is quoted in the song. According to Goddard, an earlier version lacked some of the finished version's ambiguity, culminating in the line "There is a light "in your eyes" and it never goes out". Due to a dispute between the Smiths and its record label Rough Trade Records after the group completed "The Queen Is Dead", nine months passed after the release of "The Boy with the Thorn in His Side" before the group issued another single. Once the matter was resolved, Rough Trade owner Geoff Travis felt that "There Is a Light That Never Goes Out" should be