Find the area of the region bounded by the parabola y^2=2x-2 and the line y=x-5

Answer 1

There may be an easier way to do this, but this way will work.

You need to break up the area into 4 parts.

Part 1: the integral from 0 to 5 sqrt(2x-2)

Part 2: the integral from 5 to 9 sqrt(2x-2)-(x-5)

Part 3: the integral from 0 to 3 of sqrt(2x-2)...this will be a positive area number which is actually the correct value for the area between -sqrt(2x-2) and the x-axis.

Part 4: the integral from 3 to 5 of x-5...but change the sign of the answer to positive.

Then add all the parts together.