JEE MAIN - Mathematics (2022 - 28th June Evening Shift - No. 9)
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 :
$$y = 3 - \left| {x - {1 \over 2}} \right| - |x + 1|$$ and the x-axis is :
$${9 \over 4}$$
$${45 \over 16}$$
$${27 \over 8}$$
$${63 \over 16}$$
Explanation
_28th_June_Evening_Shift_en_9_1.png)
$$ y=\left\{\begin{array}{cc} 2 x-\frac{7}{2} & x<-1 \\\\ \frac{3}{2} & -1 \leq x \leq \frac{1}{2} \\\\ \frac{5}{2}-2 x & x>\frac{1}{2} \end{array}\right. $$
$$ y=3-\left|x-\frac{1}{2}\right|-|x+1| $$
Area of shaded region (required area)
$$ =\frac{1}{2}\left(3+\frac{3}{2}\right) \cdot \frac{3}{2}=\frac{27}{8} $$
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