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

Lösung

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

\frac{( x ^{2} + 1 ) ^{\frac{3}{2}} - x ^{3}}{3}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{x^{2}}^{x^{2} + 1} u^{2} d u

Wende die Potenzregel an

= [\frac{u ^{3}}{3}]_{x^{2}}^{x^{2} + 1}

Wende Radikal Regel an:

n a^{n} = a,

angenommen

a \geq 0

= [\frac{u ^{3}}{3}]_{x}^{x^{2} + 1}

Berechne die Grenzen:

\frac{( x ^{2} + 1 ) ^{\frac{3}{2}}}{3} - \frac{x ^{3}}{3}

= \frac{( x ^{2} + 1 ) ^{\frac{3}{2}}}{3} - \frac{x ^{3}}{3}

Vereinfache

= \frac{( x ^{2} + 1 ) ^{\frac{3}{2}} - x ^{3}}{3}

\int_{0}^{r} (b r + c) (2 π r) d r

\int_{0}^{4} x^{2} + 4 d x

\int_{0}^{t} sin (u) sin (t - u) d u

\int_{6}^{100} 2 x^{- 3} d x

\int_{1}^{e} 4 t^{3} ln (t) d t