https://file.aiquickdraw.com/mathbot/file/1728510495515emowpj8x.jpg

can you solve this and show me the graph:

The graph above shows the parabola \( y = x(x - 4) \), with the area shaded between the curve and the x-axis from \( x = 0 \) to \( x = 5 \). The dashed green line marks \( x = 5 \), which is the right boundary of the region for which we computed the area.

The total area, as calculated earlier, is:

\[
A = \frac{25}{3} \, \text{square units}
\]

Would you like any further details or explanations on this? Here are some related questions you might find helpful:

1. How would the area change if the right boundary was at \( x = 6 \)?
2. Can you explain how to handle negative areas in integrals?
3. What would happen if the parabola opened downwards?
4. How can we compute the area between two curves?
5. What is the geometric interpretation of the integral in this context?

**Tip:** When calculating areas between curves and axes, always account for whether the curve dips below the axis to avoid negative area contributions!

Find the total area bounded by the x-axis, the y-axis, and the equations x = 5 and y = x(x - 4).

Learn how to find the area bounded by the curve y = x(x - 4), the x-axis, the y-axis, and x = 5. This involves understanding quadratic functions and definite integrals. Suitable for high school students in Grades 10-12.

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