3/6/2024 0 Comments Integral ex2 taylor seriesThe Maclaurin series for this function is known as the binomial series. Our first goal in this section is to determine the Maclaurin series for the function f ( x ) = ( 1 + x ) r f ( x ) = ( 1 + x ) r for all real numbers r. In one example, we consider ∫ e − x 2 d x, ∫ e − x 2 d x, an integral that arises frequently in probability theory. Second, we show how power series can be used to evaluate integrals when the antiderivative of the integrand cannot be expressed in terms of elementary functions. First, we show how power series can be used to solve differential equations. We then present two common applications of power series. In this section we show how to use those Taylor series to derive Taylor series for other functions. In the preceding section, we defined Taylor series and showed how to find the Taylor series for several common functions by explicitly calculating the coefficients of the Taylor polynomials.
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