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

Lösung

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

\frac{π x ^{2}}{4}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= x^{2} [arctan (y)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= x^{2} \frac{π}{4}

Vereinfache

= \frac{π x ^{2}}{4}

\int_{0}^{4} (2 x + 5) (3 x - 1) d x

\int_{0}^{8} x^{\frac{7}{3}} d x

\int_{1}^{2} x^{l n (x)} d x

\int_{2}^{10} 2 x^{2} d x

\int_{- 1}^{2} 3 x^{2} + 2 x - 1 d x