Area Under Curves Question 13
Question 13 - 01 February - Shift 1
Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$. Then $12 A$ is equal to
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Answer: 62
Solution:
Formula: Area between two curves - Area bounded by two intersecting curves and lines parallel to $\mathrm{y}-$ axis
$A=\int _{-1}^{0}(x^{2}-3 x) d x+\int_0^{2}(3 x-x^{2}) d x$
$\Rightarrow \quad A=\frac{x^{3}}{3}-.\frac{3 x^{2}}{2}| _{-1} ^{0}+\frac{3 x^{2}}{2}-.\frac{x^{3}}{3}|_0 ^{2}$
$\Rightarrow \quad A=\frac{11}{6}+\frac{10}{3}=\frac{31}{6}$
$\therefore \quad 12 A=62$
