integral from-x^2 to x^2+1 of f(x,y)

Lösung

\int_{- x^{2}}^{x^{2} + 1} f (x, y) d y

f, x (\frac{( 1 + x ^{2} ) ^{2}}{2} - \frac{x ^{4}}{2})

Schritte zur Lösung

\int_{- x^{2}}^{x^{2} + 1} f (x, y) d y

Entferne die Konstante:

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

= f \cdot \int_{- x^{2}}^{1 + x^{2}}, x y d y

Entferne die Konstante:

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

= f, x \cdot \int_{- x^{2}}^{1 + x^{2}} y d y

Wende die Potenzregel an

= f, x [\frac{y ^{2}}{2}]_{- x^{2}}^{1 + x^{2}}

Berechne die Grenzen:

\frac{( 1 + x ^{2} ) ^{2}}{2} - \frac{x ^{4}}{2}

= f, x (\frac{( 1 + x ^{2} ) ^{2}}{2} - \frac{x ^{4}}{2})