integral from 0 to 7 of 9x-x^2-2x

Lösung

\int_{0}^{7} 9 x - x^{2} - 2 x d x

\frac{343}{6}

Dezimale

57.16666 \dots

Schritte zur Lösung

\int_{0}^{7} 9 x - x^{2} - 2 x d x

Vereinfache

= \int_{0}^{7} - x^{2} + 7 x 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}^{7} x^{2} d x + \int_{0}^{7} 7 x d x

\int_{0}^{7} x^{2} d x = \frac{343}{3}

\int_{0}^{7} 7 x d x = \frac{343}{2}

= - \frac{343}{3} + \frac{343}{2}

Vereinfache

- \frac{343}{3} + \frac{343}{2} : \frac{343}{6}

= \frac{343}{6}

\int_{0}^{3} 3^{5 x} d x

\int_{e}^{e^{3}} \frac{ln ( x ^{3} )}{x} d x

\int_{0}^{1} 1 - e^{- x} d x

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

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