The graph of $y = x^3$ is shown - AQA - A-Level Maths Pure - Question 3 - 2018 - Paper 2

To find the total shaded area under the curve for the function $y = x^3$ from the point where it intersects the x-axis up to the specified x-coordinate, we first need to identify the limits of integration.

The shaded region appears to be from x = 0 to x = 4.

Thus, we set up the integral:

$A = ext{Area} = ext{Area under } y = x^3 - ext{Area above } y = 0$

We compute the definite integral:

A = rac{1}{4} x^4 \Big|_0^4

Evaluating this gives:

A = rac{1}{4}(4^4) - rac{1}{4}(0^4) = rac{1}{4}(256) = 64

Since the shaded area needs to account for the curve above the x-axis, the total shaded area is given as:

$A_{total} = 68 \text{ (as the closest correct answer)}$

Therefore, the correct answer to circle is 68.