Learning Target 9(CORE): I can approximate an integral using the trapezoidal rule and Simpson's rule. I can determine when each of these rules represents an overestimate or an underestimate of the actual value of an integral. I can provide an upper bound on the error produced by each of these methods. 1. Use Simpson's rule to estimate the value of the integral \(\int_{0}^{2}\frac{1}{\sqrt{1+x^{3}}} d x \) with an error of less than 0.01. You will need to first determine the number \( n \) of intervals are needed to obtain this error bound. You should use Geogebra to aid you in determining the value of \( n \). You may also use Geogebra to evaluate the function at the required values of \( x \). You must show the values you have obtained (i.e. the values of \( n \) and the values of the integrand at the appropriate values of \( x \).) When you upload your work, include a link in the comment box to the Geogebra file you used.