integral from 0 to pi/2 of cos^3(31x)

Lösung

\int_{0}^{\frac{π}{2}} cos^{3} (31 x) d x

- \frac{2}{93}

Dezimale

- 0.02150 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} cos^{3} (31 x) d x

Wende U-Substitution an

= \int_{0}^{\frac{31 π}{2}} cos^{3} (u) \frac{1}{31} d u

Entferne die Konstante:

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

= \frac{1}{31} \cdot \int_{0}^{\frac{31 π}{2}} cos^{3} (u) d u

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \frac{1}{31} \cdot \int_{0}^{\frac{31 π}{2}} (1 - sin^{2} (u)) cos (u) d u

Wende U-Substitution an

= \frac{1}{31} \cdot \int_{0}^{- 1} 1 - v^{2} d v

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= \frac{1}{31} (- \int_{- 1}^{0} 1 - v^{2} d v)

Wende die Summenregel an:

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

= \frac{1}{31} (- (\int_{- 1}^{0} 1 d v - \int_{- 1}^{0} v^{2} d v))

\int_{- 1}^{0} 1 d v = 1

\int_{- 1}^{0} v^{2} d v = \frac{1}{3}

= \frac{1}{31} (- (1 - \frac{1}{3}))

Vereinfache

\frac{1}{31} (- (1 - \frac{1}{3})) : - \frac{2}{93}

= - \frac{2}{93}

t an g e n t f (x) = ln (6 - x^{2} + 2 x^{4}), at x = 1

\frac{d y}{d x} + (\frac{3}{x}) y = - x + 4

j o in \frac{1}{3} tan^{3} (x) - tan (x) + x

x \to - 8 lim (\frac{x + 2}{x + 8})

x \to 2 lim (2 x^{2} + 7 x - 1)