Find the area enclosed by the curve y = x (x - 2) and the line y = 2x?

Answer 1

if y = x² - 2x and y = 2x the graph shows that part of the graph y = x² - 2x is below the x axis so the easy way to perform the area task is to move both curves up say 2 units, Then the equations become

y = x² - 2x + 2 and y = 2x + 2 the area between the 2 curves is the integral dydx with

y limits between x² - 2x + 2 and y = 2x + 2 and the x limits are between 0 and 4

When this integration is done, the Area = 10.67