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

User Ollifant
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1 Answer

4 votes
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
User Knubbe
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