Question
The area of the figure bounded by $${y^2} = 2x + 1$$ and $$x – y = 1$$ is :
A.
$$\frac{2}{3}$$
B.
$$\frac{4}{3}$$
C.
$$\frac{8}{3}$$
D.
$$\frac{{16}}{3}$$
Answer :
$$\frac{{16}}{3}$$
Solution :
Area of the region is given by
$$A = \int\limits_{ - 1}^3 {\left[ {\left( {y + 1} \right) - \left( {\frac{{{y^2} - 1}}{2}} \right)} \right]dy} = \frac{{16}}{3}$$
Area of the region is given by
$$A = \int\limits_{ - 1}^3 {\left[ {\left( {y + 1} \right) - \left( {\frac{{{y^2} - 1}}{2}} \right)} \right]dy} = \frac{{16}}{3}$$