integral from 0 to 20 of 4(400-y^2)

Lösung

\int_{0}^{20} 4 (400 - y^{2}) d y

\frac{64000}{3}

Dezimale

21333.33333 \dots

Schritte zur Lösung

\int_{0}^{20} 4 (400 - y^{2}) d y

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int_{0}^{20} 400 - y^{2} d y

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 4 (\int_{0}^{20} 400 d y - \int_{0}^{20} y^{2} d y)

\int_{0}^{20} 400 d y = 8000

\int_{0}^{20} y^{2} d y = \frac{8000}{3}

= 4 (8000 - \frac{8000}{3})

Vereinfache

4 (8000 - \frac{8000}{3}) : \frac{64000}{3}

= \frac{64000}{3}

\int_{5}^{2 x} ln (u) d u

\int_{0}^{\frac{1}{2}} \frac{6}{7} (2 x^{2} + x) d x

\int_{- 1}^{1} 2 e^{i αx} d x

\int_{0}^{x^{2}} t^{3} d t

\int_{0}^{\frac{π}{2}} sin (x^{4}) d x