HW4 (Graded out of 100) 1. Introduction For this program, let's explore some of the ways we can use C to perform numerical integration. We'll restrict our attention to definite integrals on smooth curves only and look at two methods, called the rectangle rule and the trapezoidal rule respectively htt en.wikipedia.org/wiki/Numerical integration With the rectangle rule, if we wish to calculate the area under a curve between two end points, a and b, we can evaluate the function at the midpoint between a and b and use that value to create a rectangle whose area will approximate the area under the curve between a and b. A diagram follows: f(a +b)/2) fox) (a +b) 2 Here, the area of the red rectangle is consider an approximation for the definite integral between a and b. This area can be expressed by the following equation: f(x) d (b- a)f When this technique is applied to a larger region of the curve, we can divide the whole large region into smaller sub-regions of equal size, and apply the rectangle rule to each one. We may get something like the following 4 2 2