Math 1001 005
Assignment 1 Solutions
1. Evaluate the following integrals:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
2 x
e + sec x tan x
3
(x4 e)2 + 1 dx =
2
dx = ex + sec x + C
3
1
2e
(x8 2ex4 + e2 + 1) dx = x9 x5 + e2 x + x + C
9
5
1
(e34t 2 cos t) dt = e34t 2 sin t
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Math 1001 005
Worksheet 2 Solutions
Practice problems not to be handed in.
1. Use the denition of the denite integral, with right endpoint tags, to evaluate
2
(2x2 x + 1) dx
2
We have that x =
2+2
n
=
4
n
and ci = 2 +
4i
.
n
Hence
2
4i
4i
2 +
+1
n
n
16i
Math 1001 005
Assignment 2
Due: Wednesday, 27 January by 4:00 in Assignment Box 23
1. Use the denition of the denite integral, with right endpoint tags, to evaluate
5
(x3 1) dx.
1
ba
n
We have that x =
f (ci ) =
6i
1 +
n
6
n
=
and ci = a + ix = 1 +
3
+ 1