Question

Find the area of the region bounded by the curve y = x³ and y = x + 6 and x = 0.

Answer 1

Given curves are y = x³, y = x + 6 and x = 0

On solving y = x³ and y = x + 6, we have

x³ = x + 6

x³ – x – 6 = 0

x²(x – 2) + 2x(x – 2) + 3(x – 2) = 0

(x – 2) (x² + 2x + 3) = 0

It’s seen that x² + 2x + 3 = 0 has no real roots

So, x = 2 is the only root for the above equation.

Now, the required area of the shaded region is given by