Find the total area of the shaded regions. Ay 30 y=x36 – 2 24 18 12- 6 ? > -10 -8 -6 4-2 2 4 6 8 10 6 -12 18 -24- 30- Find the total area of the shaded regions. ?? 14 H-2,12) 12 (2,12) Jy = 3x² 10 ob 6 4- 2- y = x – x X -4 -2 2 2 Find the total area of the shaded region. ?? 16 14 12- 10- 8 y=8 6- y=x 4 ?? 32 2- 2 6 8 B 10 12 14 16 Find the total area of the shaded regions. y 12x (3,9) 6 x – 4 2 CO -12 -18 -24 (-3, -27) –X? + 6x
The Correct Answer and Explanation is :
It looks like you’re asking about finding the total area of several shaded regions in different mathematical contexts. However, the problem you presented is a bit unclear in terms of formatting and clarity. To proceed, I need to interpret the key parts:
- You seem to be referencing multiple functions (e.g., ( y = x^2 ), ( y = x – x^2 ), and ( y = 3x^2 )).
- The area likely involves finding the regions between curves on a graph, which can be done by calculating definite integrals for each segment of the region.
- There are coordinates (e.g., (3,9), (2,12)), which may represent points where the curves intersect.
To accurately calculate the areas of these shaded regions, we would:
- Identify the curves and the intervals: For each region, find the equations of the curves that define the boundaries.
- Set up the integral(s): To find the area between the curves, set up integrals for the regions where the functions overlap.
- Calculate the definite integrals: Solve the integrals to find the areas under the curves in the specified intervals.
- Sum the areas: If there are multiple regions, sum the areas found for each one.
Since the details in your problem seem incomplete or unclear (e.g., the exact boundaries and curves for the shaded regions are not fully specified), please provide a bit more clarity. You can describe the functions and their intersections more clearly, or you can upload a more readable version of the image.
I can also generate the image if you’d like! Let me know how you’d like to proceed.