Question

The area bounded between the curve $\frac{x}{4}-\frac{y}{2}+1$, $x=-2,x=3$ and $x$-axis is:

• A. $\frac{45}{4}$
• B. $\frac{45}{2}$
• C. $15$
• D. $\frac{25}{2}$

Answer 1

The correct option is A $\frac{45}{4}$

$\frac{x}{4}$$-\frac{y}{2}+1=0$

$\frac{x}{4}+1$$=\frac{y}{2}$

$y=\frac{x}{2}+2$

$A={\int }_{-2}^3\frac{x}{2}+2dxA={[\frac{x^2}{4}+2x]}_{-2}^{3}A=[\frac{3^2}{4}+6-[\frac{(-2{)}^2}{4}-4]]A=\frac{9}{4}+6-1+4A=\frac{45}{4}$