Homework 1.pdf - University of Colorado-Boulder MATH 2300...

University of Colorado-Boulder MATH 2300 Homework 1
Turn in the following problems:
1. (a) We are a learning community that values contributions we make to each other. Write
your thoughts on the importance of submitting work that is your own.
(b) Read through the syllabus for consequences of cheating, and failing to adhere to the
standards and expectations for our learning community. Write out the policies for
cheating on written homework and quizzes.
2. Arya, Idris, and Lucy are all working to find the integral for
1
2 x
dx
Each of them use a different approach.
• Arya factors the integral
1
2 x
dx =
1
2
1
x
dx =
1
2
ln x + C
• Idris uses the substitution u = 2 x to get:
1
2 x
dx =
1
2
1
u
du =
1
2
ln 2 x + C
• Lucy uses the substitution u = 2 x to get:
1
2 x
dx =
1
u
du =
1
2
ln 2 x + C
(a) Explain why each of their approaches are valid or invalid.
(b) Explain which of the three (or all of three) correctly evaluated the integral
1
2 x
dx .