# ASSIGNMENT 3

```ASSIGNMENT 3
There are two parts to this assignment. The first part consists of 15 questions on WeBWorK — the link is
available on the course webpage. The second part consists of the questions on this page. You are expected
to provide full solutions with complete justifications. You will be graded on the mathematical, logical and
student number at the top of the first page. If your solutions are on multiple pages, the pages must be stapled
together.
Your written assignment must be handed in before the start of your recitation on Friday, January
30. The online assignment will close at 9:00 a.m. on Friday, January 30.
Z
4
Z
f (t) dt = −20. Evaluate
1. Let f (t) be continuous, with
0
2
f (2t) dt.
0
2. Find all continuous functions f (t) such that
Z
1
2 2
1
Z
f (t ) dt =
0
0
1
f (t) dt − .
3
(Hint: write the integrals in terms of the same variable.)
3. (a) Let f (t) be continuous. Prove that
Z
a
Z
0
for any constant a.
Z π
t sin(t)
π2
(b) Prove that
dt
=
.
2
4
0 1 + cos (t)
a
f (a − t)dt
f (t)dt =
0
```