integral from-4 to 1 of x^3+x^2-10x+8

Lösung

\int_{- 4}^{1} x^{3} + x^{2} - 10 x + 8 d x

\frac{875}{12}

Dezimale

72.91666 \dots

Schritte zur Lösung

\int_{- 4}^{1} x^{3} + x^{2} - 10 x + 8 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_{- 4}^{1} x^{3} d x + \int_{- 4}^{1} x^{2} d x - \int_{- 4}^{1} 10 x d x + \int_{- 4}^{1} 8 d x

\int_{- 4}^{1} x^{3} d x = - \frac{255}{4}

\int_{- 4}^{1} x^{2} d x = \frac{65}{3}

\int_{- 4}^{1} 10 x d x = - 75

\int_{- 4}^{1} 8 d x = 40

= - \frac{255}{4} + \frac{65}{3} - (- 75) + 40

Vereinfache

- \frac{255}{4} + \frac{65}{3} - (- 75) + 40 : \frac{875}{12}

= \frac{875}{12}

\int_{- 1}^{27} x^{- \frac{1}{3}} d x

\int_{0}^{6} - 3 x^{2} - 9 x + 162 d x

\int_{- 1}^{5} (3 x^{2} + 4 x) d x

\int_{2}^{3} \frac{1}{ln ( x )} d x

\int_{0}^{2 π} 3 sin (t) cos (t) d t