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Wait, That's Not Integrable!

Calculus Level 3

\[\large\int_{0}^{1}\sin x^2 \, dx\]

Which of the following series can be expressed as the value of the integral above?

Hint: Take its Macluarin series.

\[\sum_{n = 0}^{\infty} \frac{(-1)^n}{(4n + 1)(2n + 1)!}\] \[\sum_{n = 0}^{\infty} \frac{(-1)^n}{(4n + 3)(2n + 1)!}\] \[\sum_{n = 0}^{\infty} \frac{(-1)^n}{(4n + 2)(2n + 1)!}\] \[\sum_{n = 0}^{\infty} \frac{(-1)^n}{(2n + 1)!}\]

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by Andrew Ellinor

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