Question

Area bounded by the curve $y=x^2-7x+10$ and $X-$axis, is

• A. $\frac{5}{2}$
• B. $\frac{9}{2}$
• C. $\frac{7}{2}$
• D. $\frac{11}{2}$

Answer 1

The correct option is B $\frac{9}{2}$

$y=x^2-7x+10$

$\frac{dy}{dx}=2x-7y=\frac{7\pm \sqrt{49-4\left(10\right)}}{2}y=\frac{7\pm 3}{2}y=5,2$

${\int }_2^5{x}^2-7x+10dx=x$

$A={-[\frac{x^3}{3}-\frac{7x^2}{3}+10x]}_2^{5}A=-[\frac{5^3}{3}-\frac{7(5{)}^2}{3}+50-[\frac{2^3}{3}-\frac{7(2{)}^2}{3}+20]]A=-[39+30-\frac{147}{2}]A=-[69-\frac{147}{2}]$

$A=\frac{9}{2}$