{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

23-Double Integrals (General Regions)

# 23-Double Integrals (General Regions) - Double Integrals...

This preview shows pages 1–3. Sign up to view the full content.

Double Integrals: General Region I John E. Gilbert, Heather Van Ligten, and Benni Goetz As seen previously, essentially the only di ffi culty in evaluating a double integral D f ( x, y ) dxdy when D is a rectangle [ a, b ] × [ c, d ] with sides parallel to the x - and y -axes is being able to compute the single variable integrals that arise because the double integral could written as repeated single variable integrals D f ( x, y ) dxdy = d c b a f ( x, y ) dx dy = b a d c f ( x, y ) dy dx , and either choice of order of integration used, so we could always choose the more convenient one. The situation gets more complicated when D is not of the form [ a, b ] × [ c, d ] , however. It’s best to treat each region D on its own merits.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example 1: evaluate the integral I = D ( x + y ) dxdy when D consists of all points ( x, y ) such that 0 y 9 - x 2 , 0 x 3 . Good First Step: always try to draw the region D . Now y 2 = 9 - x 2 is a circle of radius 3 centered at the origin. The conditions 0 y 9 - x 2 , 0 x 3 , then show that D
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern