vcprac03s - The University of Sydney School of Mathematics...

This preview shows pages 1–2. 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: The University of Sydney School of Mathematics and Statistics Solutions to Practice Session 3 MATH2061: Vector Calculus Summer School 2012 1. Sketch the following regions: (a) { ( x, y ) ∈ R 2 | 1 ≤ x ≤ 2 , − x ≤ y ≤ x } (b) { ( x, y ) ∈ R 2 | x = r cos θ, y = r sin θ, ≤ θ ≤ 2 π, 1 ≤ r ≤ 2 } Solution: (a) 1 2 (b) 1 2 2. Describe the shaded regions as sets of points in R 2 (as in question 1 ). Use polar coordinates in part (c). (a) (b) (c) y =2 x 3 y = x 2 2 y =1- x y = x 2 Solution: (a) { ( x, y ) ∈ R 2 | ≤ x ≤ 3 , ≤ y ≤ 2 x } (b) The points of intersection of the parabola and the line are ( 1 2 , 1 4 ) and ( − 1 , 1). The shaded region is { ( x, y ) ∈ R 2 | − 1 ≤ x ≤ 1 2 , x 2 ≤ y ≤ 1- x 2 } . (c) { ( x, y ) ∈ R 2 | x = r cos θ, y = r sin θ, ≤ θ ≤ π/ 4 , ≤ r ≤ 2 } 3. Sketch the region of integration and then evaluate integraldisplay 2 integraldisplay 3 ( x − 2) sin y dx dy ....
View Full Document

{[ snackBarMessage ]}

Page1 / 4

vcprac03s - The University of Sydney School of Mathematics...

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

View Full Document
Ask a homework question - tutors are online