Chapter 3: Q. 21 (page 166)

Use the result obtained in Problem $20$ to find the area enclosed by $f (x) = - 5 x^{2} + 8$ the $x - a x i s$ and the lines $x = - 1$ and $x = 1$

Short Answer

Expert verified

The area is $12.67$ .

Step by step solution

Step 1. Given information

It is given that $f (x) = - 5 x^{2} + 8$ , we need to use the result of the problem $20$ to determine the area enclosed by $f (x)$ , the $x - a x i s$ and the lines $x = - 1$ and $x = 1$ .

Step 2. Simplify

$f (x) = - 5 x^{2} + 8$

For, $x = - 1$ ,

$f (- 1) = - 5 {(- 1)}^{2} + 8$

$= 3 = y_{0}$

For $x = 0$ ,

$f (0) = - 5 {(0)}^{2} + 8$

$= 8 = y_{1}$

For $x = 1$ ,

$y = - 5 {(1)}^{2} + 8$

$= 3$ $= y_{2}$

The area is,

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

$= \frac{1}{3} (3 + 4 \cdot 8 + 3)$

$= \frac{38}{3}$

$= 12.67$

$= \frac{38}{3}$

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Use the result obtained in Problem $20$ to find the area enclosed by $f (x) = - 5 x^{2} + 8$ the $x - a x i s$ and the lines $x = - 1$ and $x = 1$

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)=-5x2+8the x-axisand the linesx=-1andx=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

One App. One Place for Learning.

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Use the result obtained in Problem $20$ to find the area enclosed by $f (x) = - 5 x^{2} + 8$ the $x - a x i s$ and the lines $x = - 1$ and $x = 1$