integral from-1 to 1 of (ax^2+bx+c)

Lösung

\int_{- 1}^{1} (a x^{2} + b x + c) d x

2 c + \frac{2 a}{3}

Schritte zur Lösung

\int_{- 1}^{1} a x^{2} + b x + c 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}^{1} a x^{2} d x + \int_{- 1}^{1} b x d x + \int_{- 1}^{1} c d x

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

\int_{- 1}^{1} b x d x = 0

\int_{- 1}^{1} c d x = 2 c

= \frac{2 a}{3} + 0 + 2 c

Vereinfache

= 2 c + \frac{2 a}{3}

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

\int_{1}^{2} 4 x e^{x^{2} + 2} d x

\int_{0}^{1} 3 3 x d x

\int_{1}^{2} 2 y d y

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