integral from 0 to 5 of (4x-1)^2

Lösung

\int_{0}^{5} (4 x - 1)^{2} d x

\frac{1715}{3}

Dezimale

571.66666 \dots

Schritte zur Lösung

\int_{0}^{5} (4 x - 1)^{2} d x

Multipliziere aus

(4 x - 1)^{2} : 16 x^{2} - 8 x + 1

= \int_{0}^{5} 16 x^{2} - 8 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_{0}^{5} 16 x^{2} d x - \int_{0}^{5} 8 x d x + \int_{0}^{5} 1 d x

\int_{0}^{5} 16 x^{2} d x = \frac{2000}{3}

\int_{0}^{5} 8 x d x = 100

\int_{0}^{5} 1 d x = 5

= \frac{2000}{3} - 100 + 5

Vereinfache

\frac{2000}{3} - 100 + 5 : \frac{1715}{3}

= \frac{1715}{3}

\int_{2}^{10} \frac{x}{2} - \frac{2}{x} d x

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

\int_{0}^{2 π} (sin^{2} (t)) d t

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

\int_{- \frac{π}{2}}^{\frac{π}{2}} 3 cos^{3} (x) d x