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
What to the Slave Is the Fourth of July? What to the Slave Is the Fourth of July? "What to the Slave Is the Fourth of July?" is the title now given to a speech by Frederick Douglass delivered on July 5, 1852, in Corinthian Hall, Rochester, New York, addressing the Rochester Ladies' Anti-Slavery Society. The speech is perhaps the most widely known of all of Frederick Douglass' writings save his autobiographies. Many copies of one section of it, beginning in para. 32, have been circulated online. Due to this and the variant titles given to it in various places, and the fact that it is called a July