integral from 0 to 2 of 2sec((pix)/6)

Lösung

\int_{0}^{2} 2 sec (\frac{π x}{6}) d x

\frac{12}{π} ln (2 + 3)

Dezimale

5.03040 \dots

Schritte zur Lösung

\int_{0}^{2} 2 sec (\frac{π x}{6}) d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} sec (\frac{π x}{6}) d x

Wende U-Substitution an

= 2 \cdot \int_{0}^{\frac{π}{3}} sec (u) \frac{6}{π} d u

Entferne die Konstante:

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

= 2 \cdot \frac{6}{π} \cdot \int_{0}^{\frac{π}{3}} sec (u) d u

Nutze das gemeinsame Integral :

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= 2 \cdot \frac{6}{π} [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}}

Vereinfache

2 \cdot \frac{6}{π} [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}} : \frac{12}{π} [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}}

= \frac{12}{π} [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{3}}

Berechne die Grenzen:

ln (2 + 3)

= \frac{12}{π} ln (2 + 3)

t a y l or 2^{x}, 1

\int \frac{1}{θ ^{2}} sin (\frac{1}{θ}) cos (\frac{1}{θ}) d θ

\frac{d}{d t} (e^{5 t})

d er i v a t i v e y = e^{9 x}

\frac{d}{d t} (e^{t} cos (2 t))