By Philippe Dennery

First-class textual content offers thorough history in arithmetic had to comprehend modern extra complex issues in physics and engineering. issues comprise concept of services of a fancy variable, linear vector areas, tensor calculus, Fourier sequence and transforms, specified features, extra. Rigorous theoretical improvement; difficulties solved in nice element. Bibliography. 1967 variation.

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If x09 f ͑x͒ dx 37 and x09 t͑x͒ dx 16, find x09 ͓2 f ͑x͒ ϩ 3t͑x͔͒ dx. 56. y 4 y 1 0 s1 ϩ x 2 dx ഛ 51. For the function f whose graph is shown, list the following (C) x38 f ͑x͒ dx (E) f Ј͑1͒ C 2 x ͑x 2 Ϫ 4x ϩ 4͒ dx ജ 0 57. 2 ഛ quantities in increasing order, from smallest to largest, and explain your reasoning. (A) x08 f ͑x͒ dx (B) x03 f ͑x͒ dx 0 55–58 Use the properties of integrals to verify the inequality without evaluating the integrals. 0 ͭ _2 imum value M . Between what two values must x02 f ͑x͒ dx lie?

8632 From Figure 16 it appears that this estimate is better than the estimate with n 4. The Distance Problem Now let’s consider the distance problem: Find the distance traveled by an object during a certain time period if the velocity of the object is known at all times. ) If the velocity remains constant, then the distance problem is easy to solve by means of the formula distance velocity ϫ time But if the velocity varies, it’s not so easy to find the distance traveled. We investigate the problem in the following example.

Lim ͚ n l ϱ i1 a limit. (b) Use a computer algebra system to find the sum in your expression from part (a). (c) Evaluate the limit in part (a). i tan 4n 4n CAS 24. (a) Use Definition 2 to find an expression for the area under ͫ n͑n ϩ 1͒ 2 CAS ͬ 30. (a) Let A n be the area of a polygon with n equal sides uous function f from a to b, and let L n and Rn be the approximations to A with n subintervals using left and right endpoints, respectively. (a) How are A, L n, and Rn related? (b) Show that inscribed in a circle with radius r.