integral from 0 to y of integral from 0 to x of (x^2+y^2)^{3/2}

Lösung

\int_{0}^{y} \int_{0}^{x} (x^{2} + y^{2})^{\frac{3}{2}} d y d x

\frac{( 14 + 3 2 ln ( 1 + 2 ) ) y ^{5}}{40 2}

Schritte zur Lösung

\int_{0}^{y} \int_{0}^{x} (x^{2} + y^{2})^{\frac{3}{2}} d y d x

\int_{0}^{x} (x^{2} + y^{2})^{\frac{3}{2}} d y = \frac{( 3 \cdot 2 ^{\frac{1}{2}} ln ( 1 + 2 ) + 14 ) x ^{4}}{8 \cdot 2 ^{\frac{1}{2}}}

= \int_{0}^{y} \frac{( 3 \cdot 2 ^{\frac{1}{2}} ln ( 1 + 2 ) + 14 ) x ^{4}}{8 \cdot 2 ^{\frac{1}{2}}} d x

\int_{0}^{y} \frac{( 3 \cdot 2 ^{\frac{1}{2}} ln ( 1 + 2 ) + 14 ) x ^{4}}{8 \cdot 2 ^{\frac{1}{2}}} d x = \frac{( 14 + 3 2 ln ( 1 + 2 ) ) y ^{5}}{40 2}

= \frac{( 14 + 3 2 ln ( 1 + 2 ) ) y ^{5}}{40 2}

a re a 3 x, \frac{3}{4} x, 70 - x^{2}

y^{^{'}} = \frac{( y + y ^{2} )}{x ^{2}}

\int_{0}^{3} ∣ 3 x - 1 ∣ d x

\frac{\partial}{\partial x} (x^{2} + x y + 3 y)

\int (z + 1) e^{2 z} d z