(Solved): Recall that when Sn denotes the n-interval approximation for I=abf(x ...

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Recall that when $$S_n$$ denotes the $$n$$-interval approximation for $$I={?}_a^{b}f(x)dx$$ from Simpson's Rule, one has $$?I?S_n??\frac{L}{180}\frac{(b?a{)}^5}{n^4}$$ whenever $$L?\left|f^{(4)}(x)\right|$$ on $$(a,b)$$. Determine the number of intervals $$n$$ for which $$S_n$$ approximates the exact value $$I={?}_{1/10}^{1/5}\left(x^3\ln x\right)dx$$ with an absolute error of at most $$\frac{1}{3\times 10^{17}}$$. Remark: You can (and should) do this without a calculator. Give the smallest even integer $$n$$ that works, according $$n=$$