MAST10006 Calculus 2, Summer Semester, 2021
Assignment 3
School of Mathematics and Statistics, The University of Melbourne
• Submit your assignment solutions online in Gradescope (link available on LMS) before midnight 31
January 2021
• Submit your solutions as a single PDF file with the pages in the right order and correct orientation.
You may be penalised a mark if you do not.
• This assignment is worth 5% of your final MAST10006 mark.
• Marks may be awarded for:
◦ Correct use of appropriate mathematical techniques
◦ Accuracy and validity of any calculations or algebraic manipulations
◦ Clear justification or explanation of techniques and rules used
◦ Use of correct mathematical notation and terminology
• You must use methods taught in MAST10006 Calculus 2 to solve the assignment questions.
1. Evaluate the following integrals:
(a)
∫
2
x(x + 1)(x2 + 1)
dx (b)
∫
x2e2x dx.
2. Solve the first order ODE:
dy
dx
=
tanh
2
3y cosh2y
x2
(x 6= 0).
3. (NOT to be assessed) Evaluate
∫
1
e
x
2 + e
x
3 + e
x
6 + 1
dx
[End of assignment]

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