Question

The area of the region bounded by the curve x = 2y + 3, y-axis and the line y = 1 and y = -1 is
(a) 4 sq. units (b) $\frac{3}{2}$sq. units (c) 6 sq. units (d) 8 sq. units

Answer 1

To find: area of the region bounded by the curve x = 2y + 3, y-axis and the line y = 1 and y = −1



The required area of the region ABCD = ${\int }_{-1}^{1}xdy$
Thus,
$$\begin{gathered} \mathrm{Required}\mathrm{area}={\int }_{-1}^{1}xdy \\ ={\int }_{-1}^1\left(2y+3\right)dy \\ ={\left(\frac{2y^2}{2}+3y\right)}_{-1}^1 \\ =\left(1^2+3\left(1\right)\right)-\left({\left(-1\right)}^2+3\left(-1\right)\right) \\ =\left(1+3\right)-\left(1-3\right) \\ =\left(4\right)-\left(-2\right) \\ =4+2 \\ =6 \\ \mathrm{Thus},\mathrm{Area}=6\mathrm{sq}.\mathrm{units} \end{gathered}$$


Hence, the correct option is (c).