Midterm2_sample

Midterm2_sample - ) and z = 1 + x 2 + y 2 . 1 4. Find a...

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

View Full Document Right Arrow Icon
Past Exam Problems in Integrals Prof. Qiao Zhang Course 110.202 November 15, 2004 The following is a list of the problems concerning integrals that appeared in the midterm and final exams of Calc III (110.202) within the last sev- eral years. You may use them to check your understanding of the relevant material. Some other exam problems may be found at http://reserves.library.jhu.edu/access/reserves/findit/exams/110/110202.php Note: These problems do not imply, in any sense, my taste or prefer- ence for our own exam. Some of the problems here may be more (or less) challenging than what will appear in our exam. 1. Evaluate the double integral ZZ D x 2 y 2 d x d y over the triangle D with vertices (0 , 0) , (1 , 0) , (1 , 2). 2. The shape of a platform is given by x 2 + y 2 (2 - z ) 2 , 0 z 1 . (a) Describe this shape in cylindrical coordinates. (b) Find the volume of this platform. 3. Find the volume of the solid enclosed by the two paraboloids z = 2( x 2 + y 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
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) and z = 1 + x 2 + y 2 . 1 4. Find a parametrization for the surface dened by the intersection of the plane x + y + z = 1 with the cylinder x 2 + y 2 = 1. Use that parametrization to calculate the area of the surface. 5. Suppose that a particle follows the path r ( t ) = 2 cos(2 t ) i + 2 sin(2 t ) j + 3 t k . Then nd the total length of the path travelled by the particle from t = 0 to t = / 4. 6. Set up a double integral in polar coordinates to nd the volume of the solid which is bounded below by the paraboloid z = x 2 + y 2 and above by the plane z = 2 y . DO NOT EVALUATE! 7. Evaluate the integral Z 1 Z 1 y cos 1 2 x 2 d x d y. 8. Find the volume of the region under the surface z = x 2 + 2 y and over the region in the rst quadrant between the line segment connecting (0 , 2) and (2 , 0) and the curve y = 4-x 2 . 2...
View Full Document

This document was uploaded on 04/08/2012.

Page1 / 2

Midterm2_sample - ) and z = 1 + x 2 + y 2 . 1 4. Find 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