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Integrate autograph order

hello and welcome to mr. Barton's autograph video number 46 now in the last few weeks we've started to look at how autograph can help us teach differentiation and gradients and tangents and all that kind of stuff so the natural progression from that of course is to look at how autograph can handle integration and the good news is it can handle it very very well so let's take a look first thing we need is a brand new 2d graph page and if you notice from the top I'm in advanced mode now to look at Ares underneath a curve obviously first thing we need is a curve itself so I'm going to do the classic y equals x squared so click on that enter equation y equals x x 4x squared now of course as we say every week it's important for the students to predict what the codes going to look like where it goes through the shape all that kind of stuff but we'll assume a happy with that I look like okay now what I want autograph to do first is to work me out the area underneath this curve while between the curve in the x-axis from naught naught to 1 0 so the first thing we need to do is put in those points now you've a couple of options of popping in points in autograph but the best one for this is probably to select the curve itself so it goes black and then hit the coordinate tool and you'll notice you don't get a choice between your Y values here because this is gonna fix the x coordinate to the curve itself so I'd like an x value of 0 please and that should give me naught naught and then also I'm gonna hit coordinate and I'd like an x value for 1 and click OK now dead-dead simple and first I'm just gonna click on an unoccupied part of the graph area to deselect everything and to work out the area between those points underneath this curve I need to tell or to graph the two points I want so I like that point please and in whiteboard mode so another collector give me that point as well and if I right click then somewhere down here and it's right at the very bottom the screen is fine area now what's really really nice is when you introduce an integration and certainly when you're teaching the numerical methods of integration you've got all the big-name options here now I think rectangles are really nice one to start with rectangle - so I'm gonna click OK here and let's um let's see what's going on now that's a bit tricky to see from my view so let's use a bit of zoom in so little click on that drag round let's have a look at that much much better now we can see what autographs done there it's taken rectangles and with basis I think of naught point to there an issues that as an estimate of the area now we can say to the students is that a good estimate is it an under estimate and over estimate how could we improve our estimate and so on and if we actually want to look at the current value you can see it's down here area naught point two four that's a bit tricky to see so if you give that a little double-click then your slightest box comes up that area not point two for now it's a bit of a hassle if you have to keep going back in and changing the number of divisions but if you just click on and just make sure just your arrow is selected you notice you get a little lightning bolt here if I click that and what we can do is dynamically change the number of divisions and ask the students to predict as we increase the divisions what's going to happen to the estimate for the error is it going up is it going down is it going to get more realistic less accurate blah blah blah so as we increase it you'll see that the area is increasing is it going to go in it go on and definitely increase in is it going to reach a limit why is it going to reach a limit what limits are going to reach and so on so I think that's quite nice way of doing it that I will just quickly show you that you can do a very similar thing if you want to do trapezium rule and if I just select that area and give that a little delete again I'd like that point I'd like that point I'd like to right click and find area but this time I'll have trapezium rule please click OK and again we can talk about is that an overestimate or an underestimate and once again it's quite tricky to see from there but if you use the zoom in box and you just drag around one of these points you'll notice that the trapezium is over the top so it's probably going to be an over estimate that and I'm just going to undo that to get back to my original view there I am there and likewise I can do the same thing again here select my and trapeziums my little line in bulb pops up and I can increase the number of divisions and see what happens there to the area and again it seems to be reaching some kind of limit maybe if I can't be bothered with all that click and I can just cut straight to the chase 200 and you get something that seems to be quite close to 1/3 now and wouldn't it be really really nice if we could rotate that area around the x-axis and start to look at volumes of revolution well we certainly can and that's coming next week I might I'll also do next week is show you how you can find the area not just under a curve but between a curve and on line that's your little teaser to hook you in for next week but I think we'll leave it there for now and hope everything's all right take care bye-bye