integral from 0 to pi/4 of 3/(cos^2(x))

Lösung

\int_{0}^{\frac{π}{4}} \frac{3}{cos ^{2} ( x )} d x

3

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} \frac{3}{cos ^{2} ( x )} d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{\frac{π}{4}} \frac{1}{cos ^{2} ( x )} d x

Nutze das gemeinsame Integral :

\int \frac{1}{cos ^{2} ( x )} d x = tan (x)

= 3 [tan (x)]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

1

= 3 \cdot 1

Vereinfache

= 3

\int_{0}^{3} 3 t d t

\int_{0}^{2} (1 + 2 x - x^{2}) d x

\int_{0}^{t} e^{x^{2}} d x

\int_{0}^{2} 3 x (x - 4) d x

\int_{0}^{\infty} \frac{3}{x ^{2} + 5} d x