integral from a to b of |x-3|

Lösung

\int_{a}^{b} ∣ x - 3 ∣ d x

\frac{∣ b - 3 ∣ ( b - 3 ) - ∣ a - 3 ∣ ( a - 3 )}{2}

Schritte zur Lösung

\int_{a}^{b} ∣ x - 3 ∣ d x

Wende U-Substitution an

= \int_{a - 3}^{b - 3} ∣ u ∣ d u

Nutze das gemeinsame Integral :

\int ∣ u ∣ d u = \frac{u ∣ u ∣}{2}

= [\frac{u ∣ u ∣}{2}]_{a - 3}^{b - 3}

Berechne die Grenzen:

\frac{∣ b - 3 ∣ ( b - 3 )}{2} - \frac{∣ a - 3 ∣ ( a - 3 )}{2}

= \frac{∣ b - 3 ∣ ( b - 3 )}{2} - \frac{∣ a - 3 ∣ ( a - 3 )}{2}

Vereinfache

= \frac{∣ b - 3 ∣ ( b - 3 ) - ∣ a - 3 ∣ ( a - 3 )}{2}

\int_{1}^{4} x^{2} - 3 x + 2 d x

\int_{0}^{6} \frac{( 36 - x ^{2} )}{144} d x

\int_{2}^{3} \frac{x}{1 + x} d x

\int_{0}^{4} sin (x^{2}) d x

\int_{0}^{1} 10 0^{x} d x