# How to find the region bounded by the curve y = 1 - x^2 and the x axis ?

Jul 23, 2018

#### Answer:

The area of the region bounded by curve and x-axis is :
$A = \frac{4}{3} = 1.33 . s q . u n i t$

#### Explanation:

Here , curve $y = 1 - {x}^{2}$ intersect X-axes then

$y = 0 \implies 1 - {x}^{2} = 0 \implies x = \pm 1$

Let $A \left(1 , 0\right) \mathmr{and} A ' \left(- 1 , 0\right)$ be the two point of intersection of

the given curve and x-axis.

.

So, the area of the region bounded by curve and x-axis is :

color(blue)(A=|I| ,where ,I=int_a^bydx

$\therefore I = {\int}_{- 1}^{1} \left(1 - {x}^{2}\right) \mathrm{dx}$

$= 2 {\int}_{0}^{1} \left(1 - {x}^{2}\right) \mathrm{dx}$

$= 2 {\left[x - {x}^{3} / 3\right]}_{0}^{1}$

$= 2 \left[1 - {1}^{3} / 3 - 0\right]$

$= 2 \left[1 - \frac{1}{3}\right]$

$= 2 \left[\frac{2}{3}\right]$

$= \frac{4}{3}$

Hence,

$A = | \frac{4}{3} | = \frac{4}{3} \approx 1.33 . s q . u n i t s$