Question

Using integration, find the area of the region bounded between the line x = 4 and the parabola y² = 16x.

Answer 1

Given parabola and line are

y² = 16x....(i)

x = 4.....(ii)

Obviously, given parabola (i) is right handed parabola with vertex at (0, 0) and axis along +ve direction of x-axis while line (ii) is a straight line parallel to y-axis meeting x-axis at x = 4. Shaded region is required region, which is symmetric along x-axis.

\(\therefore\) Required area A is given by

A = 2(area OCAO)