Approximate the value of the definite integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of n. Round your answers to three significant digits. $\int _ { 0 } ^ { 2 } e ^ { - x ^ { 2 } } d x , n = 4$
A)a. Trapezoidal Rule: $\approx 1.881$ b. Simpson's Rule: $\approx 0.882$
B)a. Trapezoidal Rule: $\approx 0.881$ b. Simpson's Rule: $\approx 0.882$
C)a. Trapezoidal Rule: $\approx 0.881$ b. Simpson's Rule: $\approx 1.882$
D)a. Trapezoidal Rule: $\approx 0.081$ b. Simpson's Rule: $\approx 0.882$
E)a. Trapezoidal Rule: $\approx 0.881$ b. Simpson's Rule: $\approx 0.082$

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The Trapezoidal Rule and Simpson's Rule are numerical methods for approximating definite integrals. For $ n = 4 $, the Trapezoidal Rule gives approximately 0.881 and Simpson's Rule gives approximately 0.882 for the integral $\int _ { 0 } ^ { 2 } e ^ { - x ^ { 2 } } d x$.

Approximate the Value of the Definite Integral Using (A) the Trapezoidal