Question

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

Answer 1

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 Area = `int_(-2)^4 (4 + y - 1/2 y^2)"d"y`

= `|4y + y^2/2 - 1/6 y^3|_-2^4`

= 18 sq.units.