This preview shows page 1. Sign up to view the full content.
Unformatted text preview: First Exam — January 28, 2010
1 3. (10 points) Consider the integral f (x) dx, where f (x) = √ Page 6 of 11 1 + x3 . 0 (a) Estimate the error made in approximating the value of this integral using the Trapezoidal Rule
with n = 10 subintervals. State your answer in a complete sentence. You may make use of the
3x(x3 + 4)
fact that f (x) =
.
4(x3 + 1)3/2 (b) Would the Trapezoidal Rule approximation described in part (a) give an overestimate or underestimate of the actual value, or is it impossible to tell with the information given? Explain
brieﬂy. (c) Again using the Trapezoidal Rule, how many subintervals n would be necessary to guarantee an
error of at most 10−6 ? Give a valid n in simpliﬁed form. (As long as you justify your answer,
you do not have to worry about ﬁnding the best possible value.) Math 42, Winter 2010 First Exam — January 28, 2010 Page 7 of 11 4. (8 points)
(a) Set up, but do not evaluate, an integral representing the area of the region bounded by the
curves y = 5 − x2 and y = x2 + 3x + 3. As justiﬁcation, draw a picture with a sample slice
labeled. (b) Set up an integral representing the volume obtained by rotating the region from part (a) about
the xaxis. Make sure you justify your answer (draw and label a diagram). Again, don...
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.
 Spring '07
 Butscher,A
 Math, Calculus

Click to edit the document details