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Chapter 4: Q. 12 (page 402)

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible

12. The area accumulation function for a function fon an interval [a,b].

Short Answer

Expert verified

The area accumulation function for fon [a,b]is the function that, for x鈭�[a,b], is equal to the signed area between the graph of fand the x-axis on [a,b],

A(x)=鈭�axf(t)dt

Step by step solution

01

Step 1. Given data 

We have to define the area accumulation function for a function fon an interval[a,b].

02

Step 2. Definition

Let fis a continuous function on [a,b], then the area accumulation function for fon [a,b]is the function that, for x鈭�[a,b], is equal to the signed area between the graph of fand the x-axis on [a,b],

A(x)=鈭�axf(t)dt

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