integral from 0 to 1 of xsqrt(63x^2+1)

Lösung

\int_{0}^{1} x 63 x^{2} + 1 d x

\frac{73}{27}

Dezimale

2.70370 \dots

Schritte zur Lösung

\int_{0}^{1} x 63 x^{2} + 1 d x

Wende U-Substitution an

= \int_{1}^{64} \frac{u}{126} d u

Entferne die Konstante:

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

= \frac{1}{126} \cdot \int_{1}^{64} u d u

Wende die Potenzregel an

= \frac{1}{126} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{64}

Berechne die Grenzen:

\frac{1022}{3}

= \frac{1}{126} \cdot \frac{1022}{3}

Vereinfache

= \frac{73}{27}

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