Question

Determine the absolute error (as a decimal) and the relative error (as a percentage) in approximating the following integral using the trapezoidal rule with n = 4 subdivisions:

∫₋₃⁹ √(5x⁴ + 16) dx

Answer 1

To determine the absolute and relative errors, calculate the actual value of the integral using Simpson's rule as a reference. Then use the trapezoidal rule to approximate the integral and calculate the errors.

Step-by-step explanation:

In order to determine the absolute error and relative error in approximating the integral using the trapezoidal rule, we first need to calculate the actual value of the integral as a reference.

To do this, we can use a numerical integration method like Simpson's rule.

Once we have the actual value, we can use the trapezoidal rule with n = 4 subdivisions to approximate the integral and then calculate the absolute error and relative error.