de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to pi/4 of 7xsec^2(x)

Lösung

\int_{0}^{\frac{π}{4}} 7 x sec^{2} (x) d x

Lösung

7 (\frac{π}{4} - \frac{1}{2} ln (2))

+1

Dezimale

3.07177 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} 7 x sec^{2} (x) d x

Entferne die Konstante:

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

= 7 \cdot \int_{0}^{\frac{π}{4}} x sec^{2} (x) d x

Wende die partielle Integration an

= 7 [x tan (x) - \int tan (x) d x]_{0}^{\frac{π}{4}}

\int tan (x) d x = - ln ∣ cos (x) ∣

= 7 [x tan (x) - (- ln ∣ cos (x) ∣)]_{0}^{\frac{π}{4}}

Vereinfache

= 7 [x tan (x) + ln ∣ cos (x) ∣]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

\frac{π}{4} - \frac{1}{2} ln (2)

= 7 (\frac{π}{4} - \frac{1}{2} ln (2))

Graph

Beliebte Beispiele

integral from-1 to 0 of xe^x

\int_{- 1}^{0} x e^{x} d x

derivative of sqrt(\sqrt{x)}

\frac{d}{d x} (x)

integral of 2(2x+1)^6

\int 2 (2 x + 1)^{6} d x

integral of (2-2x)/(sqrt(10x-5x^2))

\int \frac{2 - 2 x}{10 x - 5 x ^{2}} d x

integral from 0 to 2 of 2pi(x)(2x-x^2)

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