Let the area of the region (x,y):2y x^2+3,y+|x| 3,y |x-1| be A.

Question

Let the area of the region

$(x,y):2y\le {x}^{2}+3,y+|x|\le 3,y\ge |x-1|$ be $A$. Then $6A$ is equal to :

Accepted Answer

$A \Rightarrow$ Rectangle ABDE $-$ Area of region EDC

$$\begin{aligned}
& A \Rightarrow 4-2 \int_0^1(3-x)-\left(\frac{x^2+3}{2}\right) d x \
& A \Rightarrow 4-2\left\{3 x-\frac{x^2}{2}-\frac{x^3}{6}-\frac{3}{2} x\right\}_0^1 \
& A \Rightarrow 4-2\left\{3-\frac{1}{2}-\frac{1}{6}-\frac{3}{2}\right\}=\frac{7}{3}
\end{aligned}$$

So $6 \mathrm{~A}=14$

Solutions · 1