a9 solu - MATH 251-3 Fall 2007 Simon Fraser University...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 251-3, Fall 2007 Simon Fraser University Assignment 9: Solutions Additional Question Due: 4:30pm, Monday 26 November 2007 1. Sketch the region of integration, and evaluate the following integral: Z 4 Z 2 √ y √ y cos( x 4 ) + x sin y dxdy Solution: The region of integration is the region above the x-axis and below the parabola x = √ y , that is, y = x 2 , for x between 0 and 2 (thus y is between 0 and 4). We are unable to integrate cos( x 4 ) with respect to x ; it has no elementary anti-derivative. However, we can try to change the order of integration. (This is necessary for the first term in the integrand; for the x sin y term, the order of integration seems immaterial, though integrating first with respect to x , then y will require an integration by parts.) Sketching the region and changing the order, we find Z 4 Z 2 √ y √ y cos( x 4 ) + x sin y dxdy = Z 2 Z x 2 √ y cos( x 4 ) + x sin y dydx = Z 2 2 3 y 3 / 2 cos( x 4 )- x cos y x 2 y =0 dx = Z 2 2 3 x 3 cos( x 4 )...
View Full Document

This note was uploaded on 10/09/2009 for the course MATH macm 101 taught by Professor Jcliu during the Spring '09 term at Simon Fraser.

Page1 / 2

a9 solu - MATH 251-3 Fall 2007 Simon Fraser University...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online