The area of the region bounded by the curve \(y = x + 1\), x-axis and the lines \(x = 2\) and \(x = 3\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{7}{2}\) sq. units
For \(2 \le x \le 3\) the line \(y = x + 1\) is above the x-axis, so the area is
\( \displaystyle A = \int_{2}^{3} (x + 1)\,dx = \left[\frac{x^2}{2} + x\right]_{2}^{3} \)
\( \displaystyle A = \left(\frac{9}{2} + 3\right) - (2 + 2) \)
\( \displaystyle A = \frac{15}{2} - 4 = \frac{7}{2} \)
Shortcut: The region is a trapezium with parallel sides y(2) = 3 and y(3) = 4 and width 1:
\( \displaystyle A = \frac{1}{2}(3 + 4)(1) = \frac{7}{2} \)
NCERT Exemplar:
Application of Integrals
