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

Lösung

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

\frac{π}{4}

Dezimale

0.78539 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

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

Wende integrale Substitution an

= 2 \cdot \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

= 2 \cdot \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)

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

Vereinfache

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

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

Berechne die Grenzen:

\frac{π}{4}

= \frac{π}{4}

\frac{d}{d x} ((2 x - 1) (3 - 4 x))

\int \frac{2}{1 - sin ( x )} d x

\int - 0.01 x d x

\int \frac{( x - 2 ) 1 - x ^{2}}{1 - x ^{2}} d x

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