Chapter 3: Q. 23 (page 166)

Use the result obtained in Problem $20$ to find the area enclosed by $f (x) = x^{2} + 3 x + 5$ , the $x - a x i s$ and the lines $x = - 4$ and $x = 4$ .

Short Answer

Expert verified

The area is $82.67$ .

Step by step solution

Step 1. Given information

It is given that $f (x) = x^{2} + 3 x + 5$ , 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 $x = - 4$ and $x = 4$ .

Step 2. Simplify

$f (x) = x^{2} + 3 x + 5$

For $x = - 4$ ,

$y_{0} = {(4)}^{2} + 3 \cdot (- 4) + 5$

$= 9$

For $x = 0$ ,

$y_{1} = {(0)}^{2} + 3 (0) + 5$

$= 5$

For $x = 4$ ,

$y_{2} = {(4)}^{2} + 3 (4) + 5$

$= 33$

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

$= \frac{2}{3} (9 + 4 \cdot 5 + 33)$

$= \frac{248}{3}$

$= 82.67$ .

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Use the result obtained in Problem $20$ to find the area enclosed by $f (x) = x^{2} + 3 x + 5$ , the $x - a x i s$ and the lines $x = - 4$ and $x = 4$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

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Use the result obtained in Problem 20to find the area enclosed by f(x)=x2+3x+5, the x-axisand the lines x=-4andx=4.

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

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Use the result obtained in Problem $20$ to find the area enclosed by $f (x) = x^{2} + 3 x + 5$ , the $x - a x i s$ and the lines $x = - 4$ and $x = 4$ .