These notes, taken for Mathematics 1B for Engineers (MAM1021S), serve as a comprehensive resource for the course. They are compiled from both in-class lectures and provided notes from the instructor. The content is structured in a sequential manner, covering the entire syllabus of the course. These...
&Seco
+ Secostanza
=
do let u =
Seco + tand
Secoct fansc
du = Secostano + seco
du doc
S -
= dx
*
u
=
Stau =
(n(u) + C
=
In/secx + tanxl + C
, mens
Integrals with Trig functions
Ex .
/sinGcosodo let u = sin O
=
cost
Su
=
=
sin C
Ex .
(secit)ton(t) de let u
=
Sec(t)
n -
sec(t)tcn(t)
=
Su
-
dt
=
↳ us + C
=
-se(t) + c
Ex
.
(cos(0) do * cos20 =
2 coo -
I
Cos20 + 1 =
cosO
= (cos (20) + 1 do Z
-
(tsin(20) + 0) + C
-
* sin(20) +
4 + C
, mens
Integrals with Trig functions
Ex .
[sin 0 cos'6 ao
-
u =
=
sin O
CosO =
I
du
-2
3 I
Sus COSO
=
cos O do dO
COS O
-
Su (1 Sus-
7
=>
-
sir 8) du
=
u du
-jut -**
I
+
C
-sin'o -Tsin8 + C
We can use this whenever we want to
[sin" (0). cos" (8)
integrate 90 B p or
q
is Odd
Ex .
(sin" (x) .
cos" (3) as
*
sin" (c)
S . . cos(c)
(x)
=
cos dx
=
(sin "(x)
*
. (cos"(x))" . cos(o) do
=
S sin" (x). (1 -
sinpcl)". cos() doc
let u =
sin(x) = cossc
=
S 434(1 -
12)"du
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