the areas of the trapezoids shown in fig now constitute our approximation to the integral ( ) : : /dt : : : : : ( where : : / : : / : : / : : ( ( ( ( with td each term in ( is readily computed and our approximate computation gives /dt : ( compared to the true answer of this is off by about howevernote that we used just trapezoids to approximate the area with more trapezoidsthe approximation would have become bettersince the straight line segments in the upper trapezoid side then would follow the graph more closely doing another hand calculation with more trapezoids is not too tempting for lazy humanthoughbut it is perfect job for computerlet us therefore derive the expressions for approximating the integral by an arbitrary number of trapezoids the general formula rb for given function /we want to approximate the integral /dx by trapezoids (of equal widthwe start out with ( and approximate each integral on the right hand side with single trapezoid in detailzb zx xdx zx /dx zxn /dx /dxxn  ch :: xn xn ch (