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

Lösung

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

33

Dezimale

5.19615 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

\int sec^{2} (u) d u = tan (u)

= 3 [tan (u)]_{0}^{\frac{π}{3}}

Berechne die Grenzen:

3

= 33

e^{- x} y \frac{d y}{d x} = e^{- y} + e^{- 2 x - y}

\int \frac{4 e ^{3 x}}{1 + e ^{3 x}} d x

im pl i c i t \frac{d y}{d x}, 2 x^{2} + 2 x + x y = 1

\frac{\partial}{\partial x} (A^{2} x^{2} + B^{2} y^{2})

(sin^{3} (t))^{^{'}}