MA223_2007FALL_EXAM1__[0] - PRACTICE MIDTERM If some of...

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: PRACTICE MIDTERM If some of these problems have multiple parts, you should be happy because otherwise they would have been 1 problem that doesnt walk you through the steps to solve it. Step 1: Please understand exactly what the problem means . Maybe even sketch some things. Step 2: Figure out what you need to find, and the calculations you need to set up to find them. Step 3: Do the calculations. And youre done with the problem. 1. Sketch the region of integration for 1 1 2 y xy dxdy e x . Evaluate the integral, but please do it by first reversing the order of integration. A: 1 1 2 y xy dxdy e x = 1 0 0 2 x xy dydx e x = 1 2 dx xe x = 1 2 1 du e u = 2 1- e . 2. a) Find the area of the region bounded by the curve x 2 + y 2 = 1, to the right of x = 0 and above the line y = 0. b) Now, find the center of this region, by averaging: integrate x over the entire region and divide by the area found in a). Similarly for y . Put the results together into a vector. Thus you have found the average of the position vector ( x , y ). Realize why. A: a) 4 2 2 cos 1 cos 1 2 / 2 / 2 1 2 = + = =- dt t dt t dx x But then, we already knew this was a quarter of the unit disk....
View Full Document

Page1 / 4

MA223_2007FALL_EXAM1__[0] - PRACTICE MIDTERM If some of...

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