⌠ x

 π t 2

S(x) :=  sin
 dt
2




⌡0
⌠ x

2
 sin π t  dt

 2 


⌡0
d
S(x)
dx
 π x 2
sin

 2 
d
2
dx
2
 πx
π x cos

 2 
x
⌠
 1 π t 2
sin
S := x → 

 dt

2



⌡0
2
 1
Sprime := sin π x 
 2

2
 1
Sdoubleprime := cos π x  π x
 2

2
S(x)
 π x 2
sin

 2 
x :=
2n
2n
2n
(-1)
n~
π
2
n~
n~
π
2
n~
2n
2n
-(-1)
2n
πx
2
2
nπ
1
0.5
0
-3
-2
-1
0
1
2
x
-0.5
-1
x :=
πx
2
2n+1
2
π
2
2n+1
3
5
x
7
3
9
5
11
7
2
13
9
11
3
15
10
5
0
-4
-2
0
2
4
x
-5
-10
-15
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
x
0.7383849958
f := x → piecewise(x < 0, 0, x ≤ 1, x, x ≤ 2, 2 - x, 0)
1

 0
 x

 2-x
 0

x<0
x≤1
x≤2
otherwise
⌠
g := x → 
⌡
x
f(t) dt
0

0

1 x2


2

1 2

 2x- x -1
2


1
x≤0
x≤1
x≤2
2<x
1
0.8
0.6
0.4
0.2
0
-2
-1
0
1
2
3