integral from 1 to 2 of 25-(t-5)^2

Lösung

\int_{1}^{2} 25 - (t - 5)^{2} d t

\frac{38}{3}

Dezimale

12.66666 \dots

Schritte zur Lösung

\int_{1}^{2} 25 - (t - 5)^{2} d t

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}^{2} 25 d t - \int_{1}^{2} (t - 5)^{2} d t

\int_{1}^{2} 25 d t = 25

\int_{1}^{2} (t - 5)^{2} d t = \frac{37}{3}

= 25 - \frac{37}{3}

Vereinfache

25 - \frac{37}{3} : \frac{38}{3}

= \frac{38}{3}