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Chapter 3: Q. 24 (page 166)

Use the result obtained in Problem 20to find the area enclosed by f(x)=-x2+x+4, thex-axisand the linesx=-1andx=1.

Short Answer

Expert verified

The area is7.33.

Step by step solution

01

Step 1. Given information

It is given that f(x)=-x2+x+4, we need to use the result obtained in Problem 20to determine the area enclosed by f(x), thex-axisand the linesx=-1andx=1.

02

Step 2. Simplify

f(x)=-x2+x+4

For x=-1,

y0=-(-1)2+(-1)+4

=2

For x=0,

y1=-(0)2+0+4

=4

For x=1,

y2=-(1)2+1+4

=4

So, Area =13(y0+4y1+y2)

=13(2+4路4+4)

=223

=7.33

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Most popular questions from this chapter

In Problems 25鈥�32, use the given functions f and g.

(a)f(x)=0(b)g(x)=0(c)f(x)=g(x)(d)f(x)>0

(e)g(x)鈮�0(f)f(x)>g(x)(g)f(x)鈮�1

f(x)=-x2+3g(x)=-3x+3

Plot the points (1,5),(2,6),(3,9),(1,12)in the Cartesian plane. Is the relation {(1,5),(2,6),(3,9),(1,12)}a function? Why?

If f(x)=x2-4, findf(-2).

Graphy=2x-3.

Match each graph to one the following functions.

f(x)=-x2-1
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