integral from 4 to 9 of 1/2 y^{1/2}+1/2 y^{-1/2}

Lösung

\int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} + \frac{1}{2} y^{- \frac{1}{2}} d y

\frac{22}{3}

Dezimale

7.33333 \dots

Schritte zur Lösung

\int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} + \frac{1}{2} y^{- \frac{1}{2}} d y

Wende die Summenregel an:

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

= \int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} d y + \int_{4}^{9} \frac{1}{2} y^{- \frac{1}{2}} d y

\int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} d y = \frac{19}{3}

\int_{4}^{9} \frac{1}{2} y^{- \frac{1}{2}} d y = 1

= \frac{19}{3} + 1

Vereinfache

\frac{19}{3} + 1 : \frac{22}{3}

= \frac{22}{3}

\frac{d}{d x} (a (2 e^{- 2 x} x - 2 e^{- 2 x} x^{2}))

\int_{- 2}^{4} x + 2 d x

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