integral from-2 to 2 of (2x-1)^2

Lösung

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

\frac{76}{3}

Dezimale

25.33333 \dots

Schritte zur Lösung

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

Multipliziere aus

(2 x - 1)^{2} : 4 x^{2} - 4 x + 1

= \int_{- 2}^{2} 4 x^{2} - 4 x + 1 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_{- 2}^{2} 4 x^{2} d x - \int_{- 2}^{2} 4 x d x + \int_{- 2}^{2} 1 d x

\int_{- 2}^{2} 4 x^{2} d x = \frac{64}{3}

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

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

= \frac{64}{3} - 0 + 4

Vereinfache

\frac{64}{3} - 0 + 4 : \frac{76}{3}

= \frac{76}{3}

\int_{0}^{1} cos^{2} (a x) d x

\int_{1}^{\infty} \frac{5}{x ^{5}} d x

\int_{0}^{1} 5 (1 - y)^{4} d y

\int_{1}^{\infty} \frac{5}{x ^{2} + 9} d x

\int_{0}^{x} \frac{cos ( t ) - 1}{t} d t