PROGRAM AREA ************************************************************************ * Program to approximate the integral of a function over the interval * * [A,B] using the trapezoidal method. Identifiers used are: * * A, B : the endpoints of the interval of integration * * N : the number of subintervals used * * I : counter * * DELX : the length of the subintervals * * X : a point of subdivision * * Y : the value of the function at X * * SUM : the approximating sum * * F : the integrand * * * * Input: A, B, and N * * Output: Approximation to integral of F on [A, B] * ************************************************************************ REAL F, A, B, DELX, X, Y, SUM INTEGER N, I PRINT *, 'ENTER THE INTERVAL ENDPOINTS AND THE # OF SUBINTERVALS' READ *, A, B, N * Calculate subinterval length * and initialize the approximating SUM and X DELX = (B - A) / REAL(N) X = A SUM = 0.0 * Now calculate and display the sum DO 10 I = 1, N - 1 X = X + DELX Y = F(X) SUM = SUM + Y 10 CONTINUE SUM = DELX * ((F(A) + F(B)) / 2.0 + SUM) PRINT 20, N, SUM 20 FORMAT (1X, 'APPROXIMATE VALUE USING', I4, + ' SUBINTERVALS IS', F10.5) END ** F(X) ********* * The integrand * ***************** FUNCTION F(X) REAL F, X F = X**2 + 1 END