integral from-3 to 5 of (2x+15)-x^2

Lösung

\int_{- 3}^{5} (2 x + 15) - x^{2} d x

\frac{256}{3}

Dezimale

85.33333 \dots

Schritte zur Lösung

\int_{- 3}^{5} 2 x + 15 - 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_{- 3}^{5} 2 x d x + \int_{- 3}^{5} 15 d x - \int_{- 3}^{5} x^{2} d x

\int_{- 3}^{5} 2 x d x = 16

\int_{- 3}^{5} 15 d x = 120

\int_{- 3}^{5} x^{2} d x = \frac{152}{3}

= 16 + 120 - \frac{152}{3}

Vereinfache

16 + 120 - \frac{152}{3} : \frac{256}{3}

= \frac{256}{3}

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

\int_{0}^{1} 6 x^{5} (9 - x^{6}) d x

\int_{0}^{1} 4 x (x^{2} + 3)^{3} d x

\int_{1}^{2} 2 x ln (x) d x

\int_{0}^{\frac{π}{2}} sin (x) sin (2 x) d x