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 than that. I was listening to what the Velvet Underground were listening to". AllMusic's Tim DiGravina argues that while depressed characters were a regular feature in Morrissey's work, his lyrics on "There Is a Light" "ups the sad-and-doomed quotient by leaps and bounds." Goddard argues in his book "Songs That Saved Your Life" that the basic narrative story is similar to that of the James Dean film "Rebel Without a Cause", in which Dean—an idol of Morrissey's—leaves his tortuous home life, being the passenger to a potential romantic partner. In fact, a line from that movie ("It is not my