Unformatted text preview: s . Its crosssections perpendicular to an altitude are equilateral triangles. Express its volume V as an integral, and ﬁnd a formula for V in terms of h and s . Verify that your answer is (1 / 3)(area of base)(height). 13. The base of a solid is the region between f ( x ) = cos x and g ( x ) =cos x ,π/ 2 ≤ x ≤ π/ 2, and its crosssections perpendicular to the xaxis are squares. Find the volume of the solid. ⇒ 9.4 Average value of a function The average of some ﬁnite set of values is a familiar concept. If, for example, the class scores on a quiz are 10, 9, 10, 8, 7, 5, 7, 6, 3, 2, 7, 8, then the average score is the sum of these numbers divided by the size of the class: average score = 10 + 9 + 10 + 8 + 7 + 5 + 7 + 6 + 3 + 2 + 7 + 8 12 = 82 12 ≈ 6 . 83 . Suppose that between t = 0 and t = 1 the speed of an object is sin( πt ). What is the average speed of the object over that time? The question sounds as if it must make sense,...
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 Fall '07
 JonathanRogawski
 Math, Calculus, average score, Ellipsoids.

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