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calculate the integral of:e(x^2/2)

Question

calculate the integral of:

  • e(x^2/2) 
check_circleAnswer
Step 1

We'll use the Maclaurin series expansion for e^(x^2/2).

3
e 1x
+..
2! 3!
3
2
2
+
3!
e 2 1+
2
+...
2!
4
x
+
2 22.2! 23.3!
6
x
e 2 1
+...
help_outline

Image Transcriptionclose

3 e 1x +.. 2! 3! 3 2 2 + 3! e 2 1+ 2 +... 2! 4 x + 2 22.2! 23.3! 6 x e 2 1 +...

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Step 2

Then integrated the series expansion. [where c...

6
e dx = 1+
+... dr
2 22.2! 2.3!
x
+
e dx x
+ ...} +c
+
2(3) 2.2!(5) 2.3!(7)
(2n+1)
Je dx=2)(n!)(2n+1)
+c
8
help_outline

Image Transcriptionclose

6 e dx = 1+ +... dr 2 22.2! 2.3! x + e dx x + ...} +c + 2(3) 2.2!(5) 2.3!(7) (2n+1) Je dx=2)(n!)(2n+1) +c 8

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Tagged in

Math

Calculus

Integration

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