100hw5soln

100hw5soln - Math 100 Homework 5 fall 2010 1. Let f be a...

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 100 Homework 5 fall 2010 1. Let f be a function in two variables defined by f ( x, y ) = 1- x , R is the region consisting of points ( x, y ) satisfying y 2 ≤ x ≤ 1 and- 1 ≤ y ≤ 1. Then, f ( x, y ) ≥ 0 when ( x, y ) belongs to R , and the given solid is the collection of points ( x, y, z ) so that ( x, y ) belongs to R and 0 ≤ z ≤ f ( x, y ). Its volume is R R f = R 1- 1 R 1 y 2 (1- x ) dxdy = R 1- 1 [1- y 2- 1 2 (1- y 4 )] dy = 8 / 15 . 2. Let R be the region collecting points ( x, y ) satisfying 0 ≤ y ≤ ln x and 1 ≤ x ≤ e . Then, the given integral is infact R R f . Alternatively, this region R collects points ( x, y ) satisfying e y ≤ x ≤ 1 and 0 ≤ y ≤ 1. Therefore, Z e 1 Z ln x f ( x, y ) dydx = Z R f ( x, y ) dxdy = Z 1 Z 1 e y f ( x, y ) dydx. 3. Let R be the region collecting points ( x, y ) satisfying- p 4- y 2 ≤ x ≤ p 4- y 2 and- 2 ≤ y ≤ 2. That is, R is the disc with radius 2 centered at the origin. It collects points whose polar coordinates (at the origin....
View Full Document

Page1 / 2

100hw5soln - Math 100 Homework 5 fall 2010 1. Let f be a...

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