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Chapter 14: Q. 16 (page 908)

Write the integral that represents the shaded area. Do not attempt to evaluate

Short Answer

Expert verified

The required integral is鈭�14-x2+5x+3dx

Step by step solution

01

Step 1. Given  information

We are given a graph of a functionf(x)=-x2+5x+3

We need to find the integral that represents its area.

02

Step 2. Integral Value Of Area

It is clear from the graph that the given function is f(x)=-x2+5x+3

and the boundaries area=1andb=4

Also, we know,

鈭�abf(x)dx

Therefore, the required integral is

鈭�14-x2+5x+3dx

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Most popular questions from this chapter

In Problem, graph each function. Use the graph to find the indicated limit, if it exists.

limx鈫�0f(x),f(x)=sinxifx鈮�0x2ifx>0

In Problems 43-52, find the limit as xapproaches cof the average rate of change of each function from cto x.

f(x)=1x2

Find limit algebraically:limx鈫�-32x3

In Problems 43-52, find the limit as xapproaches cof the average rate of change of each function from cto x.

c=1;f(x)=1x

In Problems 13鈥�32, use the accompanying graph ofy=f(x).

Findf(2)andf(6).
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