 Let's take a look at another example of how to use the trapezoidal rule to approximate the area under a curve. Here we want to approximate the integral from 0 to 1 of square root of 1 minus x cubed dx. And we want to do that with five subdivisions. So let's take a look at the graph of that and what exactly we're trying to do. So here is the curve from 0 to 1 of square root of 1 minus x cubed. And if we want five subdivisions, that would mark the end of each of our trapezoids and then of course the fifth trapezoid would end at 1. If you think about how the formula for area of a trapezoid goes, we know we need to have a multiplier of one half and then the height of each of these trapezoids is going to be given to us by b minus a over n, where n is the number of subdivisions. So we have zero minus one over five, which is a fifth or point two, which makes sense because the way I have this broken up, this would be point two, point four, point six, point eight, and then one. So the height of each of our trapezoids, if you return your head to the left, is going to be point two. So let's go ahead and start setting up our formula. Recall that use of the trapezoidal rule is only an approximation. So therefore you do need your approximately equal to symbol. Use of the squiglies for that is, of course, acceptable. So as we were saying, we need a multiplier of one half because of the actual formula for area of a trapezoid. The height of each one, as we talked about, is point two, or you could use one fifth, either one of course is fine. And then we need to start in with the sums of the bases. So the base of the first trapezoid is going to be given to us by the function value at zero. And then you might recall we have to start doubling the rest of the bases because, for instance, this first trapezoid that ends right here at point two, this is the base of the first trapezoid, but the top of the second trapezoid. When we turn to the function value we'll need at point four. That also has to get doubled because this is, it's going to serve as the bottom base of the second trapezoid and yet the top base of the third trapezoid. And we continue on in that manner. And then finally when we get to the end, the function value at one is serving only as the base for that final trapezoid and so it is only needed once. The part that you see here in the square brackets we will go ahead and do in our graphing calculator so that we do not have to round off until the very end. And then of course we'll need to multiply once we have that by half and point two. So let's switch to the graphing calculator and go ahead and do that. You'll want to have your function under y1 and then if you go to your quit screen we're going to type out that part we had written in square brackets. So the first thing we need is the function value at zero. So remember you hit vars then cross the top to yvars into function and y1. Again it looks just like your f of x function notation y1 at zero plus and now we start with having to multiply these bases by two. So we have two times the function value at point two. Of course you could do fractions if you prefer plus two times. Now we need the function value at point four plus two times the function value at point six. Plus two times the function value at point eight. And finally the function value at the end at one. And hopefully that's what you get for your answer. Now remember we still had to multiply by a half from the half that was included as part of the area formula for a trapezoid. And then also the point two the one-fifth that was the height of each trapezoid individually. So in the end for our answer we have an approximation of point eight zero nine for the area under the curve.