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Beliebt Rechnen >

integral from 0 to 1 of 1/(4+x^2)

Lösung

\int_{0}^{1} \frac{1}{4 + x ^{2}} d x

Lösung

\frac{1}{2} arctan (\frac{1}{2})

+1

Dezimale

0.23182 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1}{4 + x ^{2}} d x

Wende integrale Substitution an

= \int_{0}^{\frac{1}{2}} \frac{1}{2 ( u ^{2} + 1 )} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{1}{2}} \frac{1}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= \frac{1}{2} [arctan (u)]_{0}^{\frac{1}{2}}

Berechne die Grenzen:

arctan (\frac{1}{2})

= \frac{1}{2} arctan (\frac{1}{2})

Graph

Beliebte Beispiele

limit as x approaches 0 of (1/x+1)^x

x \to 0 lim ((\frac{1}{x} + 1)^{x})

limit as x approaches-5 of sqrt((2x^2+7x-15)/(x^2-25))

x \to - 5 lim (\frac{2 x ^{2} + 7 x - 15}{x ^{2} - 25})

(dy)/(dx)=(4sec(y))/((x+3)^2)

\frac{d y}{d x} = \frac{4 sec ( y )}{( x + 3 ) ^{2}}

integral of 1/(sqrt(4x^2+9))

\int \frac{1}{4 x ^{2} + 9} d x

integral of 1/(sqrt(9x^2-1))

\int \frac{1}{9 x ^{2} - 1} d x