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Apply the formula: $e^x$$=\sum_{n=0}^{\infty } \frac{x^n}{n!}$, where $2.718281828459045=e$, $x=-x^2$ and $2.718281828459045^x=e^{-x^2}$
Learn how to solve intégrales définies problems step by step online.
$\int\sum_{0}^{2}_{n=0}^{\infty } \frac{\left(-x^2\right)^n}{n!}dx$
Learn how to solve intégrales définies problems step by step online. int(e^(-x^2))dx&0&2. Apply the formula: e^x=\sum_{n=0}^{\infty } \frac{x^n}{n!}, where 2.718281828459045=e, x=-x^2 and 2.718281828459045^x=e^{-x^2}. Apply the formula: \left(ab\right)^n=a^nb^n, where a=-1 and b=x^2. Simplify \left(x^2\right)^n using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals n. Apply the formula: \int\sum_{a}^{b} \frac{x}{c}dx=\sum_{a}^{b} \frac{1}{c}\int xdx, where a=n=0, b=\infty , c=n! and x={\left(-1\right)}^nx^{2n}.
