Question

Find the area bounded by the curve $x = 2 - y - y^2$ and y-axis.

• A. $-\frac{9}{2}$
• B. $\frac{9}{2}$
• C. $9$
• D. $-9$

Answer 1

Answer: (B)

$\frac{9}{2}$

Answer 2

Put $2 - y - y^2 = 0$ $\Rightarrow y = 1, - 2$ This means, the curve intersects the y-axis at $y = 1$ and $y = - 2$. Hence required area $= \int\limits^{1}_{-2} xdy$ $= \int\limits^{1}_{-2} \left(2-y-y^{2}\right)dy$ $= \left[2y-\frac{y^{2}}{2}-\frac{y^{3}}{3}\right]^{1}_{-2} = \frac{9}{2}$ s units