integral from-0 to+5 of x/(sqrt(4+x^2))

Lösung

\int_{- 0}^{+ 5} \frac{x}{4 + x ^{2}} d x

29 - 2

Dezimale

3.38516 \dots

Schritte zur Lösung

\int_{- 0}^{5} \frac{x}{4 + x ^{2}} d x

Wende U-Substitution an

= \int_{4}^{29} \frac{1}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{4}^{29} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{4}^{29}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= \frac{1}{2} [2 u]_{4}^{29}

Berechne die Grenzen:

229 - 4

= \frac{1}{2} (229 - 4)

Vereinfache

= 29 - 2

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

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

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

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

\int_{0}^{3} k x^{2} + \frac{1}{30} d x