Take home question solution: Find the size of n necessary to approximate the integral 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 to within 0.0001 of the actual integral with Simpsons rule then use the n you find to compute the value. You will want to use the error approximation given in class. restart:with(student):f:=x->exp(x^2);fx:=D(f);fxx:=D(fx);fxxx:=D(fxx);fxxxx:=D(fxxx);fxxxxx:=D(fxxxx);maximize(fxxxx(x),x=3..4);minimize(fxxxx(x),x=3..4);K:=maximize(fxxxx(x),x=3..4);n:=round(evalf((K*(4-3)^5)/(180*.0001))^(1/4));Simp:=evalf(simpson(f(x),x=3..4,n));Actual:=evalf(int(f(x),x=3..4));err:=Simp-Actual;So, at least to the number of decimal points Maple returns, they are identical.