Final answer:
The trapezoidal rule is a method used to approximate the definite integral of a function by dividing the interval into subintervals and summing the areas of trapezoids formed by the curve and x-axis. For the given problem, we can use the trapezoidal rule with n = 8 to approximate the value of the integral from 0 to 2 of the function √(4-x²).
Step-by-step explanation:
The trapezoidal rule is a method used to approximate the definite integral of a function. It involves dividing the interval into equal subintervals and approximating the area under the curve by summing the areas of trapezoids formed by the curve and the x-axis.
For the given problem, with n = 8, the interval is from 0 to 2 and the function is √(4-x²). We can start by calculating the width of each subinterval: Δx = (b - a) / n = (2 - 0) / 8 = 0.25.
Next, we can evaluate the function at the endpoints of each subinterval and multiply the average of the function values by the width of the subinterval to find the area of each trapezoid. Finally, we can sum up the areas of all the trapezoids to find the approximation for the integral.