integral from-1 to 1 of e^y-(y^2-9)

Lösung

\int_{- 1}^{1} e^{y} - (y^{2} - 9) d y

e - \frac{1}{e} + \frac{52}{3}

Dezimale

19.68373 \dots

Schritte zur Lösung

\int_{- 1}^{1} e^{y} - (y^{2} - 9) 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_{- 1}^{1} e^{y} d y - \int_{- 1}^{1} y^{2} - 9 d y

\int_{- 1}^{1} e^{y} d y = e - \frac{1}{e}

\int_{- 1}^{1} y^{2} - 9 d y = - \frac{52}{3}

= e - \frac{1}{e} - (- \frac{52}{3})

Vereinfache

= e - \frac{1}{e} + \frac{52}{3}

(14 - 6 y + e - 3 x) d x - 2 d y = 0

\int_{0}^{6} \frac{π}{8} (6 - x)^{2} d x

\int sin^{4} (x co) s^{2} x d x

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x \to 0 lim (\frac{sin ( 2 x )}{x})