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
Circle line party Circle line party A Circle line party is a type of subway party occasionally held on the Circle line of the London Underground. Although the time and place of these parties is planned, the event itself occurs spontaneously, as each participant decides for themselves what sort of revelry, costume, decorations, snacks, libations and guests to bring to the party. The participants decorate the carriages festively, and play music, either live or on portable sound systems, disguised to appear as normal luggage. Other activities include setting up pole-dancing poles on the trains. Free drinks, snacks and sweets are provided, often being