integral from-1 to 0 of x(3x^2+1)

Lösung

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

- \frac{5}{4}

Dezimale

- 1.25

Schritte zur Lösung

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

Multipliziere aus

x (3 x^{2} + 1) : 3 x^{3} + x

= \int_{- 1}^{0} 3 x^{3} + 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_{- 1}^{0} 3 x^{3} d x + \int_{- 1}^{0} x d x

\int_{- 1}^{0} 3 x^{3} d x = - \frac{3}{4}

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

= - \frac{3}{4} - \frac{1}{2}

Vereinfache

- \frac{3}{4} - \frac{1}{2} : - \frac{5}{4}

= - \frac{5}{4}

\int_{0}^{4 - y^{2}} 2 x y d x

\int_{0}^{x} 4 e^{- 4 x} d x

\int_{- 1}^{343} x^{- \frac{1}{3}} d x

\int_{1}^{2} 6 x^{3} d x

\int_{- 2}^{3} 6 x^{2} - 5 d x