The image shows a problem involving a right-endpoint Riemann sum for the function $f(x) = x^2$ over the interval $[3, 9]$. The Riemann sum is an approximation of the area under the curve $y = x^2$ using rectangles.

Key Points:

1. Right-Endpoint Riemann Sum: This sum uses the function values at the right endpoints of each subinterval to determine the heights of the rectangles.

2. Approximation of Area: The Riemann sum approximates the area under the curve, which represents the integral of the function $f(x) = x^2$ over the interval $[3, 9]$.

3. Calculation of Area: As the number of subintervals increases, the Riemann sum gets closer to the exact area under the curve, which can be found by evaluating the definite integral: $\int_{3}^{9} x^2 \, dx.$

Would you like me to calculate the Riemann sum or the exact area using integration? Let me know if you have any specific questions!

Further Questions:

1. How do you calculate the right-endpoint Riemann sum for a given function?
2. What are the differences between right, left, and midpoint Riemann sums?
3. How does increasing the number of subintervals affect the accuracy of the Riemann sum?
4. What is the exact area under the curve $y = x^2$ between $x = 3$ and $x = 9$?
5. How do Riemann sums relate to the concept of definite integrals?

Tip: The accuracy of Riemann sums improves with a higher number of subintervals because the rectangles better approximate the curve's shape.