w10exam1

# 29 y x 5 dx 0 y 1 y 2 n 10 you do 0 y 1 x x 30

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Sketch the region and a typical shell. 3 not have to evaluate the2expression.) 29. y x 5 dx 0, y 1, y 2 n = 10 you do 0 , y 1 x x 30. 2 0 0 y 4 ■ 31. y 32. y 1 ■ 2 ■ ■ ■ ■ ■ 1 ■ ■ 0 ■ dy 1 y2 3 2 4 0 y 2 0 y 6 ■ y y1 2 y2 dy x cos x ■ ■ ■ sin x d x ■ ■ ■ ■ ■ ■ ■ ■ (b) If the region is instead rotated about the y -axis, use the Midpoint Rule with n = 5 to estimate the volume of the resulting solid. (Again, you do not have to evaluate your expression.) Math 42, Winter 2010 First Exam — January 28, 2010 Page 9 of 11 6. (10 points) (a) Set up two distinct integrals, each in terms of a single variable, representing the area of the √ region in the ﬁrst quadrant bounded by the curves y = x3 and y = x. For each, justify your answer by drawing a picture and marking a sample slice. Don’t evaluate either integral. (b) Set up two distinct integrals, each in terms of a single variable, representing the volume of the solid obtained by rotating the region from part (a) around the line x = 1. For each, make sure you justify your answer (draw a picture, label a sample slice, and cite the method used). Don’t evaluate either integral. Math 42, Winter 2010 First Exam — January 28, 2010 Page 10 of 11 7. (8 points) A napkin ring is made by taking a...
View Full Document

## This note was uploaded on 07/31/2013 for the course MATH 42 taught by Professor Butscher,a during the Spring '07 term at Stanford.

Ask a homework question - tutors are online