Question

Find the area bounded by the line y=x and the parabola x=y^2-2y

Answer 1

yay, integrals
so since the 2nd equation is in terms of y, we differntiate with respect to y
so we see that they intersect at y=0 and y=3
so
y=x is on top so

`\int\limits^3_0 {y-(y^2-2y)} \, dy`

`\int\limits^3_0 {y-y^2+2y)} \, dy`

`\int\limits^3_0 {y^2+3y} \, dy`

`[ (1)/(3)y^3+ (3)/(2)y^2]^3_0`
9/2 is the area