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 Again" and the flute section in "There Is a Light That Never Goes Out" (originally written as a guitar part) are based on C# minor arpeggio figure. The song features an ascending F#m–A–B chord sequence that guitarist Johnny Marr took from the Rolling Stones cover of Marvin Gaye's "Hitch Hike". Marr said in 1993 that he included the figure as an "in-joke" to determine if the music press would attribute the inspiration for the part to "There She Goes Again" by the Velvet Underground, who he contended "stole" the figure from "Hitch Hike". Marr commented, "I knew I was smarter