Final answer:
To approximate the value of the integral using the trapezoidal rule, divide the interval into smaller subintervals, find function values at the endpoints of each subinterval, and sum them up. Multiply the sum by the width of each subinterval to approximate the integral value.
Step-by-step explanation:
To approximate the value of the integral using the trapezoidal rule, we divide the interval [0, 4] into smaller subintervals. Since n = 8, we divide the interval into 8 equal subintervals. The width of each subinterval h is calculated as (b-a)/n, where a is the lower limit (0) and b is the upper limit (4). So, h = (4-0)/8 = 0.5.
Next, we find the function values at the endpoints of each subinterval and sum them up. For each subinterval, we use the formula (f(x_i) + f(x_{i+1}))/2, where f(x_i) represents the function value at the lower endpoint of the subinterval and f(x_{i+1}) represents the function value at the upper endpoint of the subinterval.
Finally, we multiply the sum by the width of each subinterval (h) to approximate the integral value. Performing these calculations, we get an approximation of the integral to be 6.832.