Question

Find the area common to the parabola y² = x – 3 and the line x = 5.

Answer 1

y² = x – 3 and x = 5

The vertex of the parabola = (3, 0)

And opens at right of Y-axis.

Required area `2int_3^5y  dx`

= `2int_3^5 sqrt(x - 3)  dx`

= `2 xx 2/3[(x - 3)^(3/2)]_3^5`

= `4/3 . 2sqrt(2) - 0`

= `(8sqrt(2))/3` sq. units