integral from-4 to 4 of sqrt(3)(16-y^2)

Lösung

\int_{- 4}^{4} 3 (16 - y^{2}) d y

\frac{256}{3}

Dezimale

147.80166 \dots

Schritte zur Lösung

\int_{- 4}^{4} 3 (16 - y^{2}) d y

Entferne die Konstante:

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

= 3 \cdot \int_{- 4}^{4} 16 - 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

= 3 (\int_{- 4}^{4} 16 d y - \int_{- 4}^{4} y^{2} d y)

\int_{- 4}^{4} 16 d y = 128

\int_{- 4}^{4} y^{2} d y = \frac{128}{3}

= 3 (128 - \frac{128}{3})

Vereinfache

3 (128 - \frac{128}{3}) : \frac{256}{3}

= \frac{256}{3}

\frac{d}{d x} (\frac{2 x ^{2} + x - 3}{2 x + 7})

\int x^{2} e^{2} d x

t an g e n t f (x) = x^{2} + 2, (3, 11)

\frac{d y}{d x} = (3 x)

\frac{d}{d x} (cot (4 x^{2}) (x^{2} - 9))