Page 535 - Modelling in Transport Phenomena A Conceptual Approach
P. 535
A.8. METHODS OF INTEGRATION 515
a b
X
Figure A.5 Values of the function f(z) at five equally spaced points.
Trapezoidal rule
In this method, the required area under the solid curve is approximated by the
area under the dotted straight line (the shaded trapezoid) as shown in Figure A.6.
x
Figure A.6 The trapezoidal rule.
The area of the trapezoid is then
(A.8-6)
If this procedure is repeated at 4 equally spaced intervals given in Figure A.5, the
value of the integral is
b [f(a) + f(a + Ax)] AS + [!(a + Ax) + f(a + 2Az)I
I= 1 f(z)dz =
2 2
+ If(. + 2Az) + f(. + 3Az)l Az + + 3Azc) + f(b)l Ax (A.87)
2 2
