Question

The area bounded by the curve $y=(x-1)(x-2)(x-3),x$-axis and ordinates $x=0,x=3$ is

• A. $9/4$
• B. 11/ 4
• C. $11/2$
• D. None of these

Answer 1

Answer: (B)

$\left|\underset{0}{\overset{1}{\int }}\left(x^3-6x^2+11x-6\right)dx\right|+\underset{1}{\overset{2}{\int }}\left(x^3-6x^2+11x-6\right)dx+\left|\underset{2}{\overset{3}{\int }}\left(x^3-6x^2+11x-6\right)dx\right|$
${{{\mid \frac{x^4}{4}-2x^3+\frac{11}{2}{x}^2-6x]}_0^1\mid +\frac{x^4}{4}-2x^3+\frac{11}{2}{x}^2-6x]}_1^2+\mid \frac{x^4}{4}-2x^3+\frac{11}{2}{x}^2-6x]}_2^3\mid$
$\left|\frac{23}{4}-8\right|+\left(-2-\left(-\frac{9}{4}\right)\right)+\left|-\frac{9}{4}+2\right|=\frac{11}{4}$