Question

The area of the curve $y=x^2-5x$, lying below the $X$-axis, is $\dots$sq.units.

• A. $\frac{125}{3}$
• B. $\frac{127}{6}$
• C. $\frac{123}{6}$
• D. $\frac{125}{6}$

Answer 1

The correct option is D $\frac{125}{6}$

$y=x^2-5x$

$x(x-5)=0$

$\therefore$ It touches x axis at $x=0$ & $x=5$

Area$=-{\int }_0^5(x^2-5x)dx$

$=-{\int }_0^5(\frac{x^3}{3}-\frac{5x^2}{2})$

$=-(\frac{125}{3}-\frac{125}{2})$

$=\frac{-125(-1)}{6}$

$\therefore \frac{125}{6}$ sq. units.