Question

Find the area bounded by the curves x = 2y2 and x = 1 - y. Your work must include an integral in one variable.

Answer 1

Answer:

Hello,

in order to simplify, i have taken the inverses functions

Step-by-step explanation:

$\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}$