Question

integral from 0 to x e^t^2

use Taylor or Maclaurin series to solve

Answer 1

Well, the Maclaurin series of e^x is \[\sum_{n=0}^{\infty}x^n/n!\] You can replace x with t^2.

Answer 2

Ohp there was a multiple choice part...hold on let me pull that up

Answer 3

Okay :)

Answer 4

a.) summation x^2n/n factorial
b.) e^x^2-1
c.) x^(2n+1)/(2n+1)nfactorial
d.) x^2n+1/(n+1) factorial
e.) x^(2n+1)/(n+1)(2n)factorial

Answer 5

c d and e have summation also

Answer 6

I got c or:
\[\int\limits_{0}^{x} \sum_{n=0}^{\infty} t^{2n}/n! dt=\sum_{n=0}^{\infty}t^{2n+1}/(2n+1)n! |_0^x\]

Answer 7

Or \[\sum_{n=0}^{\infty}x^{2n+1}/(2n+1)n! \]
Your answer choice c

Answer 8

Oooo I see

Answer 9

Thank you sir!

Answer 10

I have one more question but I should go a new one so I can give you another medal lol

Answer 11

Okay :) Thank you

Answer 12

no thank you :) alright let me post it real quick...