The area of the bounded region enclosed by the curve [y = 3 - | x - 1 2 | - |x + 1|] and t…

Question

The area of the bounded region enclosed by the curve

$$y = 3 - \left| {x - {1 \over 2}} \right| - |x + 1|$$ and the x-axis is :

Accepted Answer

$$
y=\left\{\[\begin{array}{cc} 2 x-\frac{7}{2} & x<-1 \  \ \frac{3}{2} & -1 \leq x \leq \frac{1}{2} \  \ \frac{5}{2}-2 x & x>\frac{1}{2} \end{array}$$\right.
\]

$$
y=3-\left|x-\frac{1}{2}\right|-|x+1|
$$

Area of shaded region (required area)

$$
=\frac{1}{2}\left(3+\frac{3}{2}\right) \cdot \frac{3}{2}=\frac{27}{8}
$$

Solutions · 1