integral from 0 to 1/2 of 4e^{2x}

Lösung

\int_{0}^{\frac{1}{2}} 4 e^{2 x} d x

2 (e - 1)

Dezimale

3.43656 \dots

Schritte zur Lösung

\int_{0}^{\frac{1}{2}} 4 e^{2 x} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int_{0}^{\frac{1}{2}} e^{2 x} d x

Wende U-Substitution an

= 4 \cdot \int_{0}^{1} e^{u} \frac{1}{2} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \frac{1}{2} \cdot \int_{0}^{1} e^{u} d u

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= 4 \cdot \frac{1}{2} [e^{u}]_{0}^{1}

Vereinfache

4 \cdot \frac{1}{2} [e^{u}]_{0}^{1} : 2 [e^{u}]_{0}^{1}

= 2 [e^{u}]_{0}^{1}

Berechne die Grenzen:

e - 1

= 2 (e - 1)

\int_{- 1}^{0} x (x^{2} - 1)^{10} d x

\int_{0}^{e} \frac{ln ( x ^{3} )}{x} d x

\int_{0.8}^{1} x d x

\int_{2}^{\infty} in (2 x - 3) d x

\int_{- \infty}^{0} e^{- ∣ 4 x ∣} d x