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Chapter 3: Q. 21 (page 166)

Use the result obtained in Problem 20to find the area enclosed by f(x)=-5x2+8the x-axisand the linesx=-1andx=1

Short Answer

Expert verified

The area is 12.67.

Step by step solution

01

Step 1. Given information

It is given that f(x)=-5x2+8, we need to use the result of the problem 20to determine the area enclosed byf(x), thex-axisand the linesx=-1andx=1.

02

Step 2. Simplify

f(x)=-5x2+8

For, x=-1,

f(-1)=-5(-1)2+8

=3=y0

For x=0,

f(0)=-5(0)2+8

=8=y1

For x=1,

y=-5(1)2+8

=3=y2

The area is,

Area =13(y0+4y1+y2)

=13(3+4路8+3)

=383

=12.67

=383

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Most popular questions from this chapter

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=x2-6x-1

If f(x)=14x-3,then

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In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line.

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?

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