Question

The area bounded by the x-axis and the curve $y=4x–x^2–3$ is

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{8}{3}$

Answer 1

The correct option is C $\frac{4}{3}$



$y=0,y=4x–x^2–3\Rightarrow 4x–x^2–3=0$
$\Rightarrow x^2–4x+3=0\Rightarrow (x–1)(x–3)=0\Rightarrow x=1,3$
Area = ${\int }_1^3(4x-x^2-3)dx={\left[\frac{2x^2-x^3}{3-3x}\right]}_1^3$
$=(18–9–9)–\left(\frac{2-1}{3-3}\right)=\frac{4}{3}$