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 from the Smiths' masterpiece third album, "The Queen Is Dead"." In 2014, "NME" listed "There Is a Light That Never Goes Out" as the 12th greatest song of all time. The website Acclaimed Music lists it as the 78th most acclaimed song of all time, and the 8th most acclaimed song of the 1980s. There is a chapter in Irvine Welsh's novel "Trainspotting" named after this song, which mentions its title directly. The song appears on the soundtrack to "(500) Days of Summer"; in the film, it is used to bring the main characters together. The song has been covered