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Lesson 18a - Integral Test and P-test

Lesson 18a - Integral Test and P-test - IntegralsandAreas b...

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Integrals and Areas R ll th t th j li ti f i t l i fi di th d th Recall that the major application of an integral is finding the area under the curve. This could be expressed as: b dx x f ) ( a

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Integrals and Areas W k th t if t k ti th th i t l We know that if we take a summation rather than an integral, we are approximating the area rather than finding the full area. Caution: The integral will not be the value of the sum as we are taking boxes of width 1 (not a finely defined area as done by an integral) defined area as done by an integral). Consider a graph that is strictly decreasing , positive , and continuous . We can take ti l b h i th idth f b t b 1 d h i ht t b th a partial area by choosing the width of our box to be 1, and our height to be the value of the function: This means that a 2 = f(2), a 3 = f(3) …