integral from 3 to 5 of 3t^{1/2}+4

Lösung

\int_{3}^{5} 3 t^{\frac{1}{2}} + 4 d t

10 \cdot 5^{\frac{1}{2}} - 6 \cdot 3^{\frac{1}{2}} + 8

Dezimale

19.96837 \dots

Schritte zur Lösung

\int_{3}^{5} 3 t^{\frac{1}{2}} + 4 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_{3}^{5} 3 t^{\frac{1}{2}} d t + \int_{3}^{5} 4 d t

\int_{3}^{5} 3 t^{\frac{1}{2}} d t = 10 \cdot 5^{\frac{1}{2}} - 6 \cdot 3^{\frac{1}{2}}

\int_{3}^{5} 4 d t = 8

= 10 \cdot 5^{\frac{1}{2}} - 6 \cdot 3^{\frac{1}{2}} + 8

d er i v a t i v e 4 x^{4} - \frac{1}{4 x ^{4}}

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