Question

The following plot shows a function $y$ which varies lineary with $x$. The value of the integral $I={\int }_1^{2}ydx$ is

• A. $1.0$
• B. $2.5$
• C. $4.0$
• D. $5.0$

Answer 1

The correct option is B $2.5$

$I={\int }_1^{2}ydx$
The equation of line passing thorugh $(-1,0)$ and $(0,1)$ is given by
$y-0=\frac{1-0}{0+1}(x+1)$
$y=x+1$
$I={\int }_1^2(x+1)dx$
$={[\frac{x^2}{2}+x]}_1^2$
$=2+2-\frac{1}{2}-1$
$=\frac{5}{2}=2.5$