integral from 0 to 4 of 2^{x^2}

解

\int_{0}^{4} 2^{x^{2}} d x

\frac{π erfi ( 4 ln ( 2 ) )}{2 ln ( 2 )}

解答ステップ

\int_{0}^{4} 2^{x^{2}} d x

非初等積分を使用する:

\int 2^{x^{2}} d x = \frac{π erfi ( x ln ( 2 ) )}{2 ln ( 2 )}

= \frac{π erfi ( x ln ( 2 ) )}{2 ln ( 2 )}_{0}^{4}

限度を計算する:

\frac{π}{2 ln ( 2 )} erfi (4 ln (2))

= \frac{π}{2 ln ( 2 )} erfi (4 ln (2))

簡素化

= \frac{π erfi ( 4 ln ( 2 ) )}{2 ln ( 2 )}