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 a single release by WEA to promote the "...Best II" compilation. The song reached number 25 on the UK Singles Chart, making it their last UK Top 40 appearance to date. Music critics consider "There Is a Light That Never Goes Out" to be one of the Smiths' finest efforts. Simon Goddard wrote, "In a straw poll among Smiths fans today, 'There Is a Light That Never Goes Out' would more than likely still come out victorious", which he credits to the "perfect balance" of Marr's compositional skills and Morrissey's lyricism. AllMusic's Tim DiGravina calls it "a standout among standouts