{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW15-solutions-1

HW15-solutions-1 - zakaria(mmz255 – HW15 – gilbert...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: zakaria (mmz255) – HW15 – gilbert – (55485) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Evaluate the triple integral I = integraldisplay 1 integraldisplay x integraldisplay x- y (3 x + 2 y ) dzdydx . 1. I = 5 8 2. I = 3 8 3. I = 7 24 4. I = 11 24 correct 5. I = 13 24 Explanation: As a repeated integral, I = integraldisplay 1 parenleftBig integraldisplay x parenleftBig integraldisplay x- y (3 x + 2 y ) dz parenrightBig dy parenrightBig dx . Now integraldisplay x- y (3 x + 2 y ) dz = bracketleftBig (3 x + 2 y ) z bracketrightBig x- y = (3 x + 2 y )( x- y ) = 3 x 2- xy- 2 y 2 , while integraldisplay x (3 x 2- xy- 2 y 2 ) dy = bracketleftBig 3 x 2 y- 1 2 xy 2- 2 3 y 3 bracketrightBig x = 11 6 x 3 . Consequently, I = integraldisplay 1 11 6 x 3 dx = 11 24 . keywords: integral, triple integral, re- peated integral, linear function,polynomial integrand, binomial integrand, evaluation of triple integral 002 10.0 points Evaluate the triple integral I = integraldisplay integraldisplay integraldisplay E 2 xy 2 dxdydz when E is the set of points ( x, y, z ) such that ≤ z ≤ y ≤ (4- x 2 ) 1 / 4 , and 0 ≤ x ≤ 2. 1. I = 3 2 2. I = 9 4 3. I = 2 correct 4. I = 7 4 5. I = 5 2 Explanation: As a repeated integral I = integraldisplay 2 parenleftBig integraldisplay (4- x 2 ) 1 / 4 parenleftBig integraldisplay y 2 xy 2 dz parenrightBig dy parenrightBig dx . Now integraldisplay y 2 xy 2 dz = bracketleftBig 2 xy 2 z bracketrightBig y = 2 xy 3 , while integraldisplay (4- x 2 ) 1 / 4 2 xy 3 dy = 1 2 bracketleftBig xy 4 bracketrightBig (4- x 2 ) 1 / 4 = 1 2 x (4- x 2 ) . Thus I = 1 2 integraldisplay 2 x (4- x 2 ) dx = bracketleftBig x 2- 1 8 x 4 bracketrightBig 2 . zakaria (mmz255) – HW15 – gilbert – (55485) 2 Consequently, I = 2 ....
View Full 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