

Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
A practice midterm exam for math 21d, focusing on integration and multivariable calculus. Students are required to sketch regions of integration, perform reversed integrals, integrate functions using trigonometric substitutions, find volumes of solid regions, and convert integrals to cylindrical coordinates. Problems include evaluating integrals with given limits and finding the mass of an apple using spherical coordinates.
Typology: Exams
1 / 2
This page cannot be seen from the preview
Don't miss anything!


Math 21D Name: practice midterm exam Student ID# February 2008 Section number
0
∫ (^) x
x^2
xdydx.
∫ (^1)
− 1
∫ √ 1 −x 2
−√ 1 −x^2
∫ (^) (x (^2) +y (^2) )
−(x^2 +y^2 )
21 xy^2 dzdydx