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) → \(\displaystyle\frac{5}{2}\)
For \(0 \le x \le 1\) the line \(y = x + 2\) lies above the x-axis (y goes from 2 to 3), so the area is the definite integral of y from 0 to 1.
\(\displaystyle \text{Area} = \int_{0}^{1} (x + 2)\,dx\)
\(\displaystyle = \left[\frac{x^2}{2} + 2x\right]_{0}^{1}\)
\(\displaystyle = \frac{1}{2} + 2 = \frac{5}{2}\) sq. units
Shortcut: The region is a trapezium with parallel sides y(0) = 2 and y(1) = 3 and width 1, so its area is \(\frac{1}{2}(2 + 3)(1) = \frac{5}{2}\).