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Chapter 4: Q. 30 (page 399)

For each area accumulation function A in Exercises 27鈥�30,

(a) illustrate A(2) graphically,

(b) calculate A(2) and A(5), and

(c) find an explicit elementary formula for A(x).

A(x)=鈭�-xxt3.dt

Short Answer

Expert verified

(a) The function A(2) is:

(b) The value of A(2)=0and(A(5)=0.

(c) The explicit elementary formula isA(x)=0.

Step by step solution

01

Part (a) Step 1. Given Information.

The function:

A(x)=鈭�-xxt3.dt

02

Part (a) Step 2. Graph the function.

Graph the function, A(2)=鈭�-22t3.dt

So graph the function A(2)=鈭�-22t3.dtbetween the points x=-2tox=2.

03

Part (b) Step 1. Calculate A(2). 

A(x)=鈭�-xxt3.dtA(2)=鈭�-22t3.dt=[t44]-22 =164-164=0

04

Part (b) Step 2. Calculate A(5). 

A(x)=鈭�-xxt3.dtA(5)=鈭�-55t3.dt=[t44]-55=6254-6254=0

05

Part (c) Step 1. Find an explicit formula.

Find an explicit formula for the given function.

A(x)=鈭�-xxt3.dt=[t44]-xx=x44-x44=0

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