Final Answer
$0.886227\mathrm{erf}\left(b\right)-0.886227\mathrm{erf}\left(a\right)$
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Step-by-step Solution
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1
Rewrite the function $e^{-x^2}$ as it's representation in Maclaurin series expansion
$\int\sum_{a}^{b}_{n=0}^{\infty } \frac{\left(-x^2\right)^n}{n!}dx$
Learn how to solve definite integrals problems step by step online.
$\int\sum_{a}^{b}_{n=0}^{\infty } \frac{\left(-x^2\right)^n}{n!}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function e^(-x^2) from a to b. Rewrite the function e^{-x^2} as it's representation in Maclaurin series expansion. The power of a product is equal to the product of it's factors raised to the same power. 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. We can rewrite the power series as the following.
Final Answer
$0.886227\mathrm{erf}\left(b\right)-0.886227\mathrm{erf}\left(a\right)$