Numerical Integration - Numerical Methods in Engineering with MATLAB - page 249

10.Evaluate A x 2 ydx dy over the triangle shown in Prob. 9.
11.

y

1 3

2

x

2

3 1

Evaluate A xy (2

x 2 )(2

− − xy ) dx dy over the region shown.

12. Compute A xy exp( − x 2 ) dx dy over the region shown in Prob. 11 to four dec-

imal places.
13.

y

1

x

1

Evaluate A (1 − x )( y − x ) ydx dy over the triangle shown.

14. Estimate A sin

x dx dy over the region shown in Prob. 13. Use the cubic
integration formula foratriangle. (The exact integral is 1

π

/π .)

15. Compute A sin

π π −

x ) dx dy to six decimal places, where A is the
triangular region shown in Prob. 13. Consider the triangle as adegenerate
quadrilateral.
16.

x sin ( y

y

1

1

1

x

1

Write aprogram to evaluate A

y ) dx dy overanirregular region thathas
been dividedinto severaltriangular elements. Use the program to compute
A xy ( y

f ( x ,

− x ) dx dy over the region shown.