Chapter 3: Q. 22 (page 166)

Use the result obtained in Problem $20$ to find the area enclosed by $f (x) = 2 x^{2} + 8$ , the $x - a x i s$ and the lines $x = - 2$ and $x = 2$ .

Short Answer

Expert verified

The area is $42.67$ .

Step by step solution

Step 1. Given information

It is given that $f (x) = 2 x^{2} + 8$ , we need to use the result obtained in problem $20$ to determine the area enclosed by $f (x)$ , the $x - a x i s$ and the lines $x = - 2$ and $x = 2$ .

Step 2. Simplify

$f (x) = 2 x^{2} + 8$

For $x = - 2$ ,

$y_{0} = 2 \cdot {(- 2)}^{2} + 8$

$= 16$

For $x = 0$ ,

$y_{1} = 2 \cdot {(0)}^{2} + 8$

$= 8$

For $x = 2$ ,

$y_{2} = 2 \cdot {(2)}^{2} + 8$

$= 16$

So, Area $= \frac{2}{3} (y_{0} + 4 y_{1} + y_{2})$

$= \frac{2}{3} (16 + 4 \cdot 8 + 16)$

$= \frac{128}{3}$

$= 42.67$

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x	$y = f (x)$
-2	0
-1	1
0	4
1	9
2	16

Use the result obtained in Problem $20$ to find the area enclosed by $f (x) = 2 x^{2} + 8$ , the $x - a x i s$ and the lines $x = - 2$ and $x = 2$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

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Use the result obtained in Problem20to find the area enclosed byf(x)=2x2+8, thex-axisand the linesx=-2andx=2.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Applied Mathematics

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the result obtained in Problem $20$ to find the area enclosed by $f (x) = 2 x^{2} + 8$ , the $x - a x i s$ and the lines $x = - 2$ and $x = 2$ .