Final answer:
The area of the shaded region given by x = y² - 6y can be found using integral calculus, but specific bounds are needed for a precise calculation.
Step-by-step explanation:
To find the area of the shaded region given by the equation x = y² - 6y, we would typically need to know the bounds of the region such as the range of y-values, and whether this is a region between this curve and the x-axis, another curve, or another line. Without this information, we cannot accurately determine the area. However, if we assume you need to find the area between this quadratic and the x-axis over a certain interval, we would set up an integral with respect to y from the lower bound to the upper bound of y.
For example, if we are finding the area from y = 0 to y = 6, our setup would look like this:
∫_{0}^{6} (y² - 6y) dy
Where the integral sign ∫ represents the summing up of infinitesimally small rectangles under the curve from y=0 to y=6. Integrating this function would give us a polynomial, which when evaluated at the bounds, would yield the area.