1314L18 - Lesson 18 Area and the Definite Integral We are...

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Lesson 18 – Riemann Sums and the Definite Integral 1 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. 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. 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. Next we’ll increase the number of rectangle again. 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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Lesson 18 – Riemann Sums and the Definite Integral 2 The Area Under the Graph of a Function: Let f be a nonnegative continuous function on [
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This note was uploaded on 02/15/2011 for the course MATH 1313 taught by Professor Constante during the Fall '08 term at University of Houston.

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1314L18 - Lesson 18 Area and the Definite Integral We are...

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