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Beliebt Rechnen >

integral from 3 to 5 of 1/(4+(x-3)^2)

Lösung

\int_{3}^{5} \frac{1}{4 + ( x - 3 ) ^{2}} d x

Lösung

\frac{π}{8}

+1

Dezimale

0.39269 \dots

Schritte zur Lösung

\int_{3}^{5} \frac{1}{4 + ( x - 3 ) ^{2}} d x

Wende U-Substitution an

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

Wende integrale Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

\frac{π}{4}

= \frac{1}{2} \cdot \frac{π}{4}

Vereinfache

= \frac{π}{8}

Graph

Beliebte Beispiele

y^{^{'}} + 3 y = e^{x} y^{2}

limit as x approaches 4+of (x+5)/(x-4)

x \to 4 + lim (\frac{x + 5}{x - 4})

9 y^{^{''}} + y = 0

y^{''}+4y=t^2+3e^t

y^{^{''}} + 4 y = t^{2} + 3 e^{t}

integral from 0 to pi of cos^6(x)

\int_{0}^{π} cos^{6} (x) d x