# ASU MAT 266 - mat266review_all_f2018 (6 pages)

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## mat266review_all_f2018

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- Pages:
- 6
- School:
- Arizona State University
- Course:
- Mat 266 - Calculus for Engineers II

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MAT266 Exam Review 5 5 The Substitution Rule 1 Z 6 x 4 5 dx 2 3 Suppose f is an odd function For a 0 find 6 1 Integration by Parts 4 Z 2 z ln z dz 5 Z t2 3 dt t3 9t 1 Ra a Z f x dx e2x sin x dx 6 2 Trigonometric Integrals and Substitutions 6 Z dx p 2 x 9 x2 7 Z dx p 4x2 1 8 6 3 Partial Fractions 10 Z 5x2 20x 6 dx x3 2x2 x 11 Z sin x cos x dx Z 8x3 13x dx x2 2 2 4 3 9 Z 2 p 3 p x2 3 dx x 6 4 Integration with Tables and C A S Z p u2 a2 up 2 du u 2 a2 p a2 ln u u2 2 12 Use the equation a2 C to evaluate the folZ p lowing integral x x4 9 dx Z Z du x u 13 Use the equation u ln 1 e C to evaluate the following integral dx u 1 e 1 e x2 6 5 Approximate Integration Z 14 Use the Trapezoid Rule with n 4 intervals to approximate sin d 0 Z 15 Use Simpson s Rule with n 4 intervals to approximate sin d 0 6 6 Improper Integrals Evaluate each integral below if it converges If it diverges clearly state that it diverges Z 1 Z 1 Z 1 Z 2 ex 1 dx x p dx 16 e dx 17 dx 19 18 2x 3 x 1 x 0 1 1 e 0 1 x 1 MAT266 Exam Review 7 1 Area Between Curves In each of the following find the areas between the given curves 20 y x2 2 y 21 y 2 x x 0 x 1 x2 y x 22 y 3x3 23 x 3 7 2 Volumes x2 10x y x2 2x y2 x y 1 24 Find the volume of the solid whose base is bounded by y 1 whose vertical cross sections are equilateral triangles x 2 y 1 x2 x 0 and 25 Find the volume of the solid generated by rotating the region bounded by y 2 about the line y 1 26 Find the volume of the solid generated by rotating the region bounded by y y 3 about x axis x2 y 1 p 25 x2 27 Find the volume of the solid generated by rotating the region bounded by y x2 1 y 0 x 0 x 1 about y axis 7 3 Volumes by Cylindrical Shells Using the method of cylindrical shells find the volume of the solid generated by rotating the specified region about the specified line 28 Region bounded by y x 29 Region bounded by x e y2 x3 the x axis 0 x 1 about the y axis the y axis 0 y 1 about the x axis 30 Region bounded by y x3 x 1 y 1

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