integral from 0 to 7 of (7-x)^2

Lösung

\int_{0}^{7} (7 - x)^{2} d x

\frac{343}{3}

Dezimale

114.33333 \dots

Schritte zur Lösung

\int_{0}^{7} (7 - x)^{2} d x

Multipliziere aus

(7 - x)^{2} : 49 - 14 x + x^{2}

= \int_{0}^{7} 49 - 14 x + x^{2} 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} 49 d x - \int_{0}^{7} 14 x d x + \int_{0}^{7} x^{2} d x

\int_{0}^{7} 49 d x = 343

\int_{0}^{7} 14 x d x = 343

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

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

Vereinfache

= \frac{343}{3}

\frac{d}{d x} (\frac{ln ( x )}{x ^{2}})

\frac{\partial}{\partial x} (\frac{( 2 x + y )}{x + 2 y})

\int_{0}^{π} π (sin^{2} (x))^{2} d x

\int + x ln (x) d x

a re a e^{4 x}, e^{8 x}, x = 1