The area (in sq. units) of the region bounded by the line x = 2y + 3, the y-axis and the lines y = 1 and y = 3 is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 14
The region lies between the y-axis (x = 0) and the line, from y = 1 to y = 3. For these y, \(x = 2y+3 \gt 0\), so the area is found by integrating x with respect to y:
\( \displaystyle A = \int_{1}^{3} (2y+3)\,dy \)
\( \displaystyle = \left[y^{2}+3y\right]_{1}^{3} \)
\(= (9+9) - (1+3)\)
\(= 14\)