Numerical Integration - Numerical Methods in Engineering with MATLAB - page 248

4. Use third-order Gauss-Legendrequadraturetoobtain an approximate valueof

1

1

cos π

( x − y )

dx dy

2

− 1 − 1

(The exact value of the integral is 1 . 621 139.)

5.

y

4

4

x

2

Map the integral A xydx dy from the quadrilateral region shown to the “stan-
dard” rectangle and then evaluate it analytically.

6.

y

4

4

x

2 3

Compute A x dx dy over the quadrilateral region shown by first mapping it into
the “standard” rectangle and thenintegrating analytically.

7.

y

4

3

x

2

Use quadraturetocompute A x 2 dx dy over the triangle shown.
8. Evaluate A x 3 dx dy over the triangle shown in Prob. 7.
9.

y

4

x

3

Evaluate A (3 − x ) ydx dy over the region shown.