integral from 50 to 100 of x/(27+4x^2)

Lösung

\int_{50}^{100} \frac{x}{27 + 4 x ^{2}} d x

\frac{1}{8} (ln (40027) - ln (10027))

Dezimale

0.17303 \dots

Schritte zur Lösung

\int_{50}^{100} \frac{x}{27 + 4 x ^{2}} d x

Wende U-Substitution an

= \int_{10027}^{40027} \frac{1}{8 u} d u

Entferne die Konstante:

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

= \frac{1}{8} \cdot \int_{10027}^{40027} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{8} [ln ∣ u ∣]_{10027}^{40027}

Berechne die Grenzen:

ln (40027) - ln (10027)

= \frac{1}{8} (ln (40027) - ln (10027))

\int_{x}^{1} e^{\frac{x}{y}} d y

\int_{- 2}^{1} (3 - y^{2}) - (y + 1) d y

\int_{7}^{9} x^{2} + 2 x - 5 d x

\int_{0}^{x + z} 6 x z d y

\int_{- 2}^{2} (e^{x} - e^{- x}) d x