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Find the area of the region bounded by the parabola y2 = 2x and the straight line x – y = 4.

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The intersecting points of the given curves are obtained by solving the equations x – y = 4 and y2 = 2x for x and y.

We have y2 = 8 + 2y i.e., (y – 4) (y + 2) = 0 which gives y = 4, –2 and x = 8, 2.

Thus, the points of intersection are (8, 4), (2, –2). Hence

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