integral from y to 2y of 8x+e^y

פתרון

\int_{y}^{2 y} 8 x + e^{y} d x

y e^{y} + 12 y^{2}

צעדי פתרון

\int_{y}^{2 y} 8 x + e^{y} d x

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

:הפעל את תכונת הליניאריות

= \int_{y}^{2 y} e^{y} d x + \int_{y}^{2 y} 8 x d x

\int_{y}^{2 y} e^{y} d x = y e^{y}

\int_{y}^{2 y} 8 x d x = 12 y^{2}

= y e^{y} + 12 y^{2}

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