Graphics Programs Reference
In-Depth Information
Solution
y
12
4
c
10
a
10
b
x
y
) isquadratic, quadratureover the three integrationpoints shown
in Fig. 6.10(b) will besufficientforan“exact”result. Note that the integrationpoints
lie in the middle of each side; their coordinates are(6
Because
f
(
x
,
,
10), (8
,
5) and (14
,
15). The area
of the triangle isobtained fromEq. (6.49):
111
x
1
111
0 16 12
0 10 20
1
2
1
2
A
=
=
=
100
x
2
x
3
y
1
y
2
y
3
FromEq. (6.51) we get
c
I
=
A
W
k
f
(
x
k
,
y
k
)
k
=
a
100
1
15)
1
3
f
(8
1
3
f
(14
=
3
f
(6
,
10)
+
,
5)
+
,
3
(6
2
15
2
)
=
100
10
2
)
(8
2
5
2
)
(14
2
=
−
+
−
+
−
1800
PROBLEM SET 6.3
1.
Use Gauss-Legendrequadraturetocompute
1
1
x
2
)(1
y
2
)
dx dy
(1
−
−
−
1
−
1
2. Evaluate the following integral with Gauss-Legendrequadrature:
2
3
x
2
y
2
dx dy
y
=
0
x
=
0
3. Compute the approximate valueof
1
1
e
−
(
x
2
y
2
)
dx dy
+
−
1
−
1
with Gauss-Legendrequadrature. Use integration order (a)two and (b)three.
(The true value of the integral is 2
.
230 985.)
Search WWH ::
Custom Search