Using integration find the area of the region bounded between the line x=2 and the parabola y2 = 8x

You can this in 2 ways: either along x axis which would ease the situation as the area would be calculated using the even function property of the integrable area, i.e. same magnitude of area on both sides of x axis but with different polarities.

Second is along y axis : Calculate the area bounded by the intercept of the parabola with the line across y axis and Subtract from it the area bounded by the parabola across the y axis.