MA101 Lecture 6: Lab Week 6 Solutions
Document Summary
Ma101 week 6 report - applications of integration; substitution. Winter 2014: [5 marks] consider the integral w = xe1 3x2 dx. (cid:90) (a) load the student package in maple and de ne the above integral as follows: with(student): w:=int(x*exp(1-3*x 2),x); (b) determine an appropriate substitution to try: 6xdx (c) use maple"s changevar command to apply this substitution and write maple"s output below. 6 (d) have maple evaluate the integral using the command value(%). What is missing from maple"s answer (but must be included in yours)? w = 1. Maple does not include the constant of integration. (e) we must express our nal answer in terms of the original variable, x. We can do this in maple using the subs command, and your original substitution. e1 3x2 subs(u=?? xe1 3x2. 6 (cid:90: [5 marks] in a recently stocked sh pond, the sh population growth rate is given by: , 0 t 12 where t is in months.
