integral from 0 to 5 of (sqrt(x-1))^2

Lösung

\int_{0}^{5} (x - 1)^{2} d x

\frac{15}{2}

Dezimale

7.5

Schritte zur Lösung

\int_{0}^{5} (x - 1)^{2} d x

Vereinfache

(x - 1)^{2} : x - 1

= \int_{0}^{5} x - 1 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{5} x d x - \int_{0}^{5} 1 d x

\int_{0}^{5} x d x = \frac{25}{2}

\int_{0}^{5} 1 d x = 5

= \frac{25}{2} - 5

Vereinfache

\frac{25}{2} - 5 : \frac{15}{2}

= \frac{15}{2}

\int_{1}^{5} \frac{1}{x ^{2} - 1} d x

\int_{- 1}^{1} x^{3} - 9 x d x

\int_{- 1}^{2} 6 x^{2} d x

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

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