Trapezoidal and Rectangular Integration

Question

im working on a program to integrate a function using rectangluar and trapezoidal integration. this is what i have little bit of so far or that i understand to calculate the trapezoidal portion of an equation. Console.WriteLine(); double lower =0; double upper = 10; DoubleFunction function = new DoubleFunction( Example.Foo ); double integral = TrapezoidalRule.Integrate( function lower upper ); Console.WriteLine( Integral from  + lower +  to  + upper +  is  + integral ); Console.ReadLine(); internal static double Foo( double d ) { return Math.Sin( d ) + ( d * d ); } the equation to INTEGRATE IS HERE: This program integrates f(x) = x^4 - 2x^3 -12x^2 + 3x + 40 over the interval 0 to 10 using rectangular and trapezoidal integration. With a sample width of 0.1 THE OUTPUT LOOKS LIKE THIS: The true value of the integral is xx.xxxxxx Using rectangular integration the integral value is yy.yyyyyy Using trapezoidal integration the integral value is zz.zzzzzzz CAN ANYONE HELP????

bn9 · Answer

Rectangular Integration with Backward Differences: If the width of a single sample is T then the area of a rectangle at point n is T times xn. If writen Yn = Yn-1 + T*Xn then we can approximate y as a succession of rectangular areas like this For trapezoidal integration divide the function into trapezoids spaced at the sample intervals. The area of a single trapezoid can be found by taking the average of the two ordinates and multiplying it by the width T. The relevant equation is: Yn = Yn-1 + T (( Xn + Xn-1) / (2))

Bill Farley · Answer

I have no idea why you are using sin(d) + d^2 to do trapezoidal or rectangular integration. Trapezoidal would be: For f(x) to f(y) (y-x being your step size): f(x)(y-x) + 1/2( (y-x) * ( f(y) - f(x) ) ) Which should be the area of a trapeziod bounded by xyf(x)f(y). No trig needed Bill F

jiggleslupiniv · Answer

Sory I don't know rectangular and Trapezoidal integration: please state the real problem and the formula of rectangular and trapezoidal integration and how I relate the sample width and sin function.