integral from 0 to (5pi)/4 of sec^4(t/5)

Lösung

\int_{0}^{\frac{5 π}{4}} sec^{4} (\frac{t}{5}) d t

\frac{20}{3}

Dezimale

6.66666 \dots

Schritte zur Lösung

\int_{0}^{\frac{5 π}{4}} sec^{4} (\frac{t}{5}) d t

Wende U-Substitution an

= \int_{0}^{\frac{π}{4}} sec^{4} (u) \cdot 5 d u

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{\frac{π}{4}} sec^{4} (u) d u

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= 5 \cdot \int_{0}^{\frac{π}{4}} (1 + tan^{2} (u)) sec^{2} (u) d u

Wende U-Substitution an

= 5 \cdot \int_{0}^{1} 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

= 5 (\int_{0}^{1} 1 d v + \int_{0}^{1} v^{2} d v)

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

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

= 5 (1 + \frac{1}{3})

Vereinfache

5 (1 + \frac{1}{3}) : \frac{20}{3}

= \frac{20}{3}

\int_{x}^{2 - x^{2}} 1 d y

\int_{1}^{2} \frac{2 ^{l n (x)}}{x} d x

\int_{1}^{3} (8 x^{3} + 6 x - 45) d x

\int_{0}^{1} \frac{2 e ^{3 x}}{7} d x

\int_{0}^{a} (b cos (c x) + d) d x