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so in this section what we need to do is really understand integration as the limit of a sum and how were going to look at that is just through an example its probably the best way to really think of it so what ive got here is a a sketch of y equals x squared plus four and ive got a specific domain between zero and eight so this is what the curve would look like so when x is zero we would have y is four when x is 8 wed have y 68 okay and what i want to do is i want to find the exact area between the curve and the x-axis so all of this bit here okay all of that area i want to find so with the tools that we currently have what i could do is i could start to estimate it using the area of rectangles so for example as a pretty poor first attempt i could draw a rectangle there is just eight wide and four high and think right that is my first estimate to this area okay so my first estimate the area will be eight wide times by four high and so that gets me 32. and clearly this is an unde
