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Beliebt Rechnen >

integral from 0 to-1 of 3/(1+t^2)

Lösung

\int_{0}^{- 1} \frac{3}{1 + t ^{2}} d t

Lösung

- \frac{3 π}{4}

+1

Dezimale

- 2.35619 \dots

Schritte zur Lösung

\int_{0}^{- 1} \frac{3}{1 + t ^{2}} d t

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 1}^{0} \frac{3}{1 + t ^{2}} d t

Entferne die Konstante:

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

= - 3 \cdot \int_{- 1}^{0} \frac{1}{1 + t ^{2}} d t

Nutze das gemeinsame Integral :

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

= - 3 [arctan (t)]_{- 1}^{0}

Berechne die Grenzen:

\frac{π}{4}

= - 3 \cdot \frac{π}{4}

Vereinfache

= - \frac{3 π}{4}

Graph

Beliebte Beispiele

integral from 1 to 4 of e^{-x}

\int_{1}^{4} e^{- x} d x

integral from-1 to 2 of-x^2

\int_{- 1}^{2} - x^{2} d x

integral from-2 to 2 of-x^2+5

\int_{- 2}^{2} - x^{2} + 5 d x

integral from 0 to 1 of 1/2 e^x+3/4 2^x

\int_{0}^{1} \frac{1}{2} e^{x} + \frac{3}{4} 2^{x} d x

integral from-3 to 7 of (|x|)

\int_{- 3}^{7} (∣ x ∣) d x