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in this video were going to focus on finding the area using the limit definition so lets say if we have the function x cube and we want to find the area of the shaded region between the x-axis and the curve over the closed interval from zero to eight so lets draw a picture so x cube on the right side looks like this and so from 0 to 8 we want to find the area of the shader region how can we do so using the limit definition well you need to know the formula to calculate the area its equal to the limit as n approaches infinity of the sum of all of the rectangles starting from 1 to n of f of x sub i times delta x delta x represents the width of the rectangle and f of x sub i is the height of the rectangle so as n becomes very large were going to use an infinite number of rectangles to approximate the area under the curve and were going to add the area of each rectangle were going to sum it up and thats going to give us the area under curve which is equal to the definite integral
