Final answer:
To express the integral as a limit of Riemann sums, we can use different methods such as the Right Riemann Sum, Left Riemann Sum, Midpoint Riemann Sum, or Trapezoidal Riemann Sum. Each method involves dividing the interval of integration into subintervals and approximating the area under the curve. The limit of these sums as the number of subintervals approaches infinity gives us the value of the integral.
Step-by-step explanation:
To express the integral as a limit of Riemann sums, we can use different methods depending on whether we want to calculate the Right Riemann Sum (option A), Left Riemann Sum (option B), Midpoint Riemann Sum (option C), or Trapezoidal Riemann Sum (option D).
Each method involves dividing the interval of integration into subintervals and approximating the area under the curve by summing the areas of rectangles or trapezoids. The limit of these sums as the number of subintervals approaches infinity gives us the value of the integral.
For example, to calculate the Right Riemann Sum, we would use the right endpoints of each subinterval to calculate the height of the rectangles. We would then sum the areas of these rectangles and take the limit as the number of subintervals approaches infinity.