Exercise
$\int_1^x\left(e^{-x^2}\right)dx$
Step-by-step Solution
Learn how to solve integrals of polynomial functions problems step by step online. Integrate the function e^(-x^2) from 1 to x. 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.
Integrate the function e^(-x^2) from 1 to x
Final answer to the exercise
$\frac{\sqrt{\pi }\mathrm{erf}\left(x\right)}{2}- \frac{\sqrt{\pi }\mathrm{erf}\left(1\right)}{2}+C_0$