DU Sure to show that all of your antiderivatives are the same (up to, perhaps, addition by a constant) once you have finished all of the evaluations. Question (3): Let R be the region bounded between the x-axis and the curve y 2+4x+3 0 2. Question (5): Consider: x2 - 4 (a) Evaluate this integral using (1) a u-substitution, (2) integration by parts, (3) a trigonometric substi- tution, and (4) using the method of partial fraction decomposition. (b) Discuss in 1-2 English sentences which method you would advise a fellow student to use and why. 572 + 77 +4
DU Sure to show that all of your antiderivatives are the same (up to, perhaps, addition by a constant) once you have finished all of the evaluations. Question (3): Let R be the region bounded between the x-axis and the curve y 2+4x+3 0 2. Question (5): Consider: x2 - 4 (a) Evaluate this integral using (1) a u-substitution, (2) integration by parts, (3) a trigonometric substi- tution, and (4) using the method of partial fraction decomposition. (b) Discuss in 1-2 English sentences which method you would advise a fellow student to use and why. 572 + 77 +4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Question 4 F please
Transcribed Image Text:DU Sure to show that all of your antiderivatives are the same (up to, perhaps, addition by a constant) once
you have finished all of the evaluations.
Question (3): Let R be the region bounded between the x-axis and the curve y 2+4x+3
0<x <1. Find the volume of the solid generated when the region R is revolved abouo
for
(a) the x-axis.
(b) the y-axis.
(c) the line x = 1.
=D1.
Question (4): Each of the following integrals will need the method of partial fractions after a u-
substitution has been made. Evaluate each integral.
(a) / Cos
cos5
dx
sin x
In x+4
(@) (In a)3 – 2(In x)² – 3 In x)
(4) /=
d.x
COS X
dx
dx
sin? x - sin
(e)/
(b)
|
e20 + et - 3
In x + 4
dx
(c) (In)2
et - 2
(c) / Inz+4
dx
(f) 2 +1
dx, x> 2.
Question (5): Consider:
x2 - 4
(a) Evaluate this integral using (1) a u-substitution, (2) integration by parts, (3) a trigonometric substi-
tution, and (4) using the method of partial fraction decomposition.
(b) Discuss in 1-2 English sentences which method you would advise a fellow student to use and why.
572 + 77 +4
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