Approximate the following integral using the indicated methods. Leave your answers in "calculator-ready" form.

∫e^(−4x^2)dx from 0 to 1

(a) Trapezoidal Rule with 4 subintervals

b) Midpoint Rule with 4 subintervals

(c) Simpson's Rule with 4 subintervals

(d) With f(x)=e^(−4x^2), It can be shown by direct computation that|f(4)(x)|≤192 on the interval [0,1]. Using this information and the error formula:

E(n)≤M(b−a)^5/(180n^4)

what is the least value of n so that the Simpson's Rule approximation for the given integral is guaranteed to be accurate to within 0.00001?