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Lesson-18-filled - Math 1314 Lesson 18 Area and the...

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Math 1314 Lesson 18 Area and the Definite Integral We are now ready to tackle the second basic question of calculus – the area question. We can easily compute the area under the graph of a function so long as the shape of the region conforms to something for which we have a formula for geometry. Example 1 : Suppose . 5 ) ( = x f Find the area under the graph of ) ( x f from . 4 to 0 = = x x Approximating Area Under a Curve Now suppose the area under the curve is not something whose area can be easily computed. We’ll need to develop a method for finding such an area. Example 2 : Here we’ll draw some rectangles to approximate the area under the curve. We can find the area of each rectangle, then add up the areas to approximate the area under the curve.
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Example 3 : Next, we’ll increase the number of rectangles. Example 4 : And we’ll increase the number of rectangles again.
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What you should see is that as the number of rectangles increases, the area we compute using this method becomes more accurate.
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