Answer to Question #345130 in Calculus for Jane

Question

Find the area bounded by the curve x=y²+2y and the line x=3.

Answer 1

Solution

Points of intersection of the given curves are solution of equation y² + 2y = 3   =>  y² + 2y – 3 = 0 => y₁ = -3, y₂ = 1.

So area between curves is

$A=\int_{-3}^{1}\left[3\ -y^2-2y\right]dy=\left[3y\ -\frac{1}{3}y^3-y^2\right]\left|\begin{matrix}1\\-3\\\end{matrix}\right.$

A = 3 – 1/3 – 1 + 9 – 9 + 9 = 11 – 1/3 = 10.66667