Use series to approximate the definite integralIto within th

Use series to approximate the definite integralIto within the indicated accuracy.

0.5	x^⁴e^(^{?x)^²}dx
$\"Use$
0

e^x = sum x^n/n!
e(-x^2)= sum (-1)^n x^2n/ n!
x^4 e^(-x^2)= sum (-1)^n x^(2n+4)/n!
Integrate and we get
sum (-1)^n x^(2n +5)/(2n+5) n!
So we have (0.5)^5/5 - (0.5)^7/7 +(.5)^9/9*2!
.00625 - .00111 = .00514
Next term is .0001

Use series to approximate the definite integralIto within the indicated accuracy. 0.5 x^4e^(?x)^2dx 0 Solutione^x = sum x^n/n! e(-x^2)= sum (-1)^n x^2n/ n! x^4

Use series to approximate the definite integralIto within th

Solution

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