A:IV>partial derivative +V - L "dxdyRecall that for a general function fx), the integral feldx representa the difference ofthe area below the curve y = f(x) but above the r-axis when f(x) 2 0, and the area above the104CHAPTER 3. MULTIPLE INTEGRALSeurve but below the r-axis when f(x)s0. Similarly, the double integral of any continuousfunetion f(x, y) represents the difference of the volume below the surface z=f(x, y) but abovethe xy-plane when f(x,y) 20, and the valume above the surface but below the xy-plane whenflz,y) s0. Thus, our method of double integration by means of iterated integrals can beused to evaluate the double integral of any continuous funetion over a rectangle, regardlessof whether fix, y)20 or not.Exumple 3.3. Evaluate [ sintx+ y)dxdy.Solution: Note that f(x,y)= sin(r+y) is both positive and negative over the rectangle [0,)(0,2n1 We can still evaluate the double integral:sin(x + yldzdy = (-conlx + y)dy(-cos(y+)+ cos y)dy- - sin(y+n)+ sin y. --sin3r + sin 27-(-sinn+ sin0)ExercisesAFor Exercises 1-4, find the volume under the surface z = ((r,y) over the rectangle R.2. fls, y)=e*, R=[0,1] -[-1,1]1. fx, y)=4xy, R=[0,1] [0,1]3. f(x, y) =x+y*.R=[0,1]x [0,1]4. fiz,y)=x*+xy + yª, R = [1,2]= [0,2)For Exercises 5-12, evaluate the given double integral.z(x+y}dxdy6.a+2)dzdyC[ zy+ sinx)dzdy7.9.xycostxy)dxdysinxcosty-)dxdy11Idxdy13. Let M be a constant. Show that Mdxdy = M(d - eXb -a).

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Por Exercises 1-4, find the volume under the surface z= (x,9) over the rectangle R. 1. (x.y)= day, R=10,1 10,1) 3. (x, y)-+y", R=(0,1) (0,1) For Exercises 5-12, evalunte the given double integral. 3. LLa-yrdzdy 2. (a.y)=e*,R=10,1)-(-1,1) 4. fta.y)=*+xy+y.R-1,2) - (0,2) LL day+ sinz)dzdy sinzcosty-nidxdy 12. LL 1drdy 8. 10. 13. Let M be a constant. Show that Mdxdy- M(d - eXb -a).

Por Exercises 1-4, find the volume under the surface z= (x,9) over the rectangle R. 1. (x.y)= day, R=10,1 10,1) 3. (x, y)-+y", R=(0,1) (0,1) For Exercises 5-12, evalunte the given double integral. 3. LLa-yrdzdy 2. (a.y)=e,R=10,1)-(-1,1) 4. fta.y)=+xy+y.R-1,2) - (0,2) LL day+ sinz)dzdy sinzcosty-nidxdy 12. LL 1drdy 8. 10. 13. Let M be a constant. Show that Mdxdy- M(d - eXb -a).

Cornerstones of Financial Accounting

4th Edition

ISBN:9781337690881

Author:Jay Rich, Jeff Jones

Publisher:Jay Rich, Jeff Jones

ChapterA1: International Financial Reporting Standards

Section: Chapter Questions

Problem 3MCQ

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