integral from 7 to 10 of y/(y^2-3y-4)

Lösung

\int_{7}^{10} \frac{y}{y ^{2} - 3 y - 4} d y

\frac{ln ( 11 ) + ln ( 2 )}{5}

Dezimale

0.61820 \dots

Schritte zur Lösung

\int_{7}^{10} \frac{y}{y ^{2} - 3 y - 4} d y

Ermittle den Partialbruch von

\frac{y}{y ^{2} - 3 y - 4} : \frac{1}{5 ( y + 1 )} + \frac{4}{5 ( y - 4 )}

= \int_{7}^{10} \frac{1}{5 ( y + 1 )} + \frac{4}{5 ( y - 4 )} 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_{7}^{10} \frac{1}{5 ( y + 1 )} d y + \int_{7}^{10} \frac{4}{5 ( y - 4 )} d y

\int_{7}^{10} \frac{1}{5 ( y + 1 )} d y = \frac{1}{5} (ln (11) - 3 ln (2))

\int_{7}^{10} \frac{4}{5 ( y - 4 )} d y = \frac{4}{5} ln (2)

= \frac{1}{5} (ln (11) - 3 ln (2)) + \frac{4}{5} ln (2)

Vereinfache

\frac{1}{5} (ln (11) - 3 ln (2)) + \frac{4}{5} ln (2) : \frac{ln ( 11 ) + ln ( 2 )}{5}

= \frac{ln ( 11 ) + ln ( 2 )}{5}

x \to + 2 lim (4 tan (3 x - 3))

\int_{6}^{9} \frac{1}{x ^{2} - 1} d x

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