2 Let S be that part of the cylindrical surface x +y 2 = 9 = 0 which lies in the first octant between the surfaces z = and z = 12 x 3* y. (a) Make a rough sketch of S. (b) Calculate the area of S using a double integral. The following steps you through it. (i) Write the cylindrical surface as F(x,y,z) = 0 and then calculate gradF. 2 x y (ii) In the expression z = substitute for either x or y. , 3 Which one is simpler? So which way will you project? Describe the region R. Decide on the order of integration. (iii) Set up the area integral and evaluate it.

2 Let S be that part of the cylindrical surface x +y 2 = 9 = 0 which lies in the first octant between the surfaces z = and z = 12 x 3* y. (a) Make a rough sketch of S. (b) Calculate the area of S using a double integral. The following steps you through it. (i) Write the cylindrical surface as F(x,y,z) = 0 and then calculate gradF. 2 x y (ii) In the expression z = substitute for either x or y. , 3 Which one is simpler? So which way will you project? Describe the region R. Decide on the order of integration. (iii) Set up the area integral and evaluate it.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Analytic Trigonometry

Section2.3: Solving Trigonometric Equations

Problem 11ECP

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