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Area Formulas

Published in: Mathematics
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  • Arman R

    • Rajkot
    • 4 Years of Experience
    • Qualification:
    • Teaches: Mathematics, Algebra
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Easy to learn with diagram

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    AP Calculus Area
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    Area of a Plane Region Calculus was built around two problems — Tangent line — Area
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    Area To approximate area, we use rectangles More rectangles means more accuracy
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    Area Can over approximate with an upper sum Or under approximate with a lower sum
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    Area Variables include — Number of rectangles used — Endpoints used
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    Area Regardless of the number of rectangles or types of inputs used, the method is basically the same. Multiply width times height and add,
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    Upper and Lower Sums An upper sum is defined as the area of circumscribed rectangles A lower sum is defined as the area of inscribed rectangles The actual area under a curve is always between these two sums or equal to one or both of them,
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    Area Approximation We wish toa roximate the area under a curve from a to b. We begin by subdividing the interval [a, b] into n subintervals. Each subinterval is of width Ax.
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    a Area Approximation b
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    Area Approximation We wish to approximate the area under a curve f from a to b. We begin by subdividing the interval [a, bl into n subintervals of width n Minimum value offin the ith subinterval f (Ml) = Maximum value offin the ith subinterval
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    Area Approximation AMI): f(mı): a Ax b
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    Area Approximation So the width of each rectangle is Ax = n i
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    AMI): f(mı): a b
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    Area Approximation So the width of each rectangle is Ax = The height of each rectangle is either f (m) i or f(Ml)
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    AMI):
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    Area Approximation So the width of each rectangle is Ax = The height of each rectangle is either f (m) i or f(Ml) So the upper and lower sums can be defined as Lower sum = s n i=l Upper sum = Ef(Mlbr
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    Area Approximation It is important to note that s(n) (Area) S(n) Neither approximation will give you the actual area Either approximation can be found to such a degree that it is accurate enough by taking the limit as n goes to infinity In other words lim lim S(n)

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