Mathematical Methods for Engineers 2 (MATH 1064)
Mathematical Methods for Engineers
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Mathematical Methods for Engineers 2 (MATH 1064)
Total: 30 marks
Late submissions without approval of the Course coordinator attract a penalty of 10% per day, up
to 40%. After 4 days the work won’t be accepted.
You are required to submit your handwritten or typed solutions as a single PDF
file using the online link on the course webpage. If you submit handwritten solutions,
make sure to write legibly and make a good scan. If you use MS Word, type all mathematical
expressions using Equation editor. Both handwritten and typed mathematical expressions must
be notationally correct and clearly presented. Marks will be deducted for poorly presented
solutions. Show your working out.
1. Use an appropriate integration technique to evaluate the following integrals.
(a)
∫ 2
0
√
2x− x2 dx (Hint: start with completing the square)
(b)
∫
ln(x2 + 1) dx
(c)
∫ 3√3
0
x2
(x2 + 9)3/2
dx
(5+5+5=15 marks)
2. Does the following improper integral converge or diverge? Explain carefully.∫ ∞
0
x3e−x
2
dx
(7 marks)
3. Find the general solution of the following differential equation.
dy
dx
=
x2
x4 − 1 , (x 6= ±1)
(8 marks)