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Integrate autograph

hello and welcome to mr. Barton's autograph video number 47 now this week we're going to continue the work that we started last week where we used autograph to introduce the concept of integration and to find the area under a curve and this week we're going to look at some two-dimensional twists that integration often throws up so when my students are happy finding the area under a curve I love to throw this little one into the mix so I asked them what would the equation y equals x squared minus 4x plus 3 look like where would it cross the x-axis where it across the y-axis where's its minimum value blah blah blah blah blah are now happy we shall draw that I'm not bothered with slope lot just to save a bit of time and then I say to locate I don't love you please to integrate me that curve between the x value of 0 and 3 and work out what you get and a few minutes pass and then a few surprised spaces may start to emerge when the end up with a value of zero and then we can start to think well why is it zero because it's clearly not zero area underneath the curve and autograph can actually lend a hand here if we get visual illustration of the area so i'm going to select the curve i'm going to right click and i'm going to go for find area and i'm going to jump straight to Simpsons rule and I'm going to jump straight to 200 divisions students don't need to know what Simpsons rule is if you just understand that it's an accurate measure for the area under the curve we can deal with that later and 200 divisions are going to give me a nice accurate reading and I'm going to go from a start point of zero to an end point of three click OK and there's my area there now if you want a reading of that if you just give the status bar and it will double click on the bottom and make sure your area is selected you'll see that the air is 1.95 blah blah blah but look times by 10 to the power of minus sixty-two is pretty much zero which is what your students will get now why is it zero well of course it's because there's some bits in the area above the curtain some bits below the curve so how are we going to find out what the actual physical size of that area is well what we're going to need to do and hopefully the students will come up with this is forget that area so give that a select and a delete we're going to need to find the area between zero and that crossing point which looks like it's 1 and 1 and that cross point which looks like it's three so let's do that let's select the curve let's right-click let's go find area and this time let's go from zero to one Simpsons rule 200 let's get that box then and now let's select the curve again right click find area and this time we'll go from one to three Simpsons rule couple of hundred click OK and now if I select that area and I just text box it and I'll go for a little bit of ice blue and click OK I get that size of areas of 1.3 2 53 and if I select that area and again I go text box it and I get a lovely bit of ice blue I see that that area is negative 1.33 and that explains why we got our strange results right got that in our heads let's do another quick one here so i'll just quickly and get a new to DeGraaf page if you want to find the area and between the covin the y-axis dead dead easy you just need an equation that starts instead of y equals startswith x equals so let's have a look at some classic like x equals y squared and again you can just hit why twice or you can do the little square thing again we'll get students to predict what it looks like blah blah blah click OK and when you've got it same deal select the curve right click find area and this time it's going to be the y axis so if we say not too long we say Simpsons rule we say 200 we get a bit of that dead dead easy and the final thing you may wish to do with integration and again I'll get myself a brand-new 2d Griffin raft page is the area between a curve and a line so let's have y equals x squared let's have the classic y equals ax and there's our little area that we don't have to find out there I can't really see that so I'm going to zoom in using my marquee zoom so give that a little drag round there that's much better and now i'm going to tell autograph that I'd love the area between that curve and that line sorry that pounding that curve both better be selected right click and hopefully you'll get find area and again it's the same deal you choose your start point use your endpoints so I'm going to go 0 0 where they cross there and one one where they cross their a bit of Simpsons rule a bit of 200 divisions click OK and there's my area that if I want to see what it is double click on that and it's that the only thing you've got to be careful of is the order that you select if I very quickly I don't have time for this but we'll give it a go if I did the curve first unknown the line and I right click and I did find area and I did Simpsons rule all 16 seconds and added 200 and i click ok then what I'm actually going to get this time I'm pretty sure is a negative error so just be careful of the order and that is integration in 2d 3d coming next week take care bye bye