integral from 1 to 4 of ln(x^2)

Lösung

\int_{1}^{4} ln (x^{2}) d x

16 ln (2) - 6

Dezimale

5.09035 \dots

Schritte zur Lösung

\int_{1}^{4} ln (x^{2}) d x

Wende die partielle Integration an

= [x ln (x^{2}) - \int 2 d x]_{1}^{4}

\int 2 d x = 2 x

= [x ln (x^{2}) - 2 x]_{1}^{4}

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

= [2 x ln (x) - 2 x]_{1}^{4}

Berechne die Grenzen:

16 ln (2) - 6

= 16 ln (2) - 6

\int_{- 1}^{1} x^{4} - x^{2} d x

\int_{- \frac{3}{2}}^{\frac{1}{2}} (x^{3} - 4 x) d x

\int_{- 2}^{3} (x + 6) - x^{2} d x

\int_{- \infty}^{- 4} θ e^{θ} d θ

\int_{0}^{1} (4 x - 3 x^{2}) d x