The area (in sq. units) of the region bounded by the line $y = x+2, x = 0, x = 1$ and $y = 0$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{5}{2}$
Given region is bounded by
$y=x+2,\;y=0,\;x=0,\;x=1$
Required area
$\int_{0}^{1}(x+2-0)\,dx$
$=\int_{0}^{1}(x+2)\,dx$
$=\left[\frac{x^2}{2}+2x\right]_{0}^{1}$
$=\frac{1}{2}+2$
$=\frac{5}{2}$
The required area is $\frac{5}{2}$ square units.