Use series to approximate the definite integral to within the indicated accuracy

Question

Use series to approximate the definite integral to within the indicated accuracy:

Note: The answer you derive here should be the partial sum of an appropriate series (the number of terms determined by an error estimate). This number is not necessarily the correct value of the integral truncated to the correct number of decimal places.

Use series to approximate the definite integral to within the indicated accuracy: Note: The answer you derive here should be the partial sum of an appropriate series (the number of terms determined by an error estimate). This number is not necessarily the correct value of the integral truncated to the correct number of decimal places. (1/4)x^4

Explanation / Answer

Since e^x = 1 +x +x^2 /2 +x^3 /3!.....

e^(-x^3)= 1 +(-x^3) +(-x^3)^2/2 +(-x^3)^3 /3!+.....

Integrating we have x - x^4/4 + x^7/14 - x*10/60+......

So we have 0.4 -(0.4)^4/4 +(0.4)^7/14

0.4 -.0064+.000117+.00000175= 0.39377

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