251sol8 - fact the right-hand edge of the triangle is the line x = t I = I 1 I t cos t 2 dx dt = I 1 b cos t 2 x B t x =0 dt = I 1 t cos t 2 dt

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Page 1 Section 15.2
Background image of page 1

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

View Full DocumentRight Arrow Icon
Page 1 Section 15.3
Background image of page 2
Page 2 Section 15.3
Background image of page 3

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

View Full DocumentRight Arrow Icon
Page 1 Section 15.4
Background image of page 4
Page 2 Section 15.4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Assignment 8 Multivariate Calculus Math 251 (Fall 2010) A1. A1. Find the average value of the function f ( x ) = i 1 x cos( t 2 ) dt on the interval [0 , 1]. Solution The average is I = 1 1 - 0 I 1 0 f ( x ) dx = I 1 0 I 1 x cos( t 2 ) dt dx. This double integral is over a region which is a triangle in the ( x, t )-plane, with vertices (0 , 0), (0 , 1), and (1 , 1). It is much easier to reverse the order of integration, and using the
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: fact the right-hand edge of the triangle is the line x = t . I = I 1 I t cos( t 2 ) dx dt = I 1 b cos( t 2 ) x B t x =0 dt = I 1 t cos( t 2 ) dt. Finally, we substitute u = t 2 so that t dt = 1 2 du . When t = 0, we have u = 0. When t = 1, we have u = 1. I = 1 2 I 1 cos u du = 1 2 (sin 1-sin 0) = sin(1) 2 . a...
View Full Document

This note was uploaded on 12/13/2010 for the course MATH 251 taught by Professor Unknown during the Spring '08 term at Simon Fraser.

Page1 / 6

251sol8 - fact the right-hand edge of the triangle is the line x = t I = I 1 I t cos t 2 dx dt = I 1 b cos t 2 x B t x =0 dt = I 1 t cos t 2 dt

This preview shows document pages 1 - 6. Sign up to view the full document.

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