integral from 2 to 4 of (xy^2+x^2+y+4)

Lösung

\int_{2}^{4} (x y^{2} + x^{2} + y + 4) d y

2 x^{2} + \frac{56 x}{3} + 14

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2}^{4} 4 d y + \int_{2}^{4} x^{2} d y + \int_{2}^{4} y d y + \int_{2}^{4} x y^{2} d y

\int_{2}^{4} 4 d y = 8

\int_{2}^{4} x^{2} d y = 2 x^{2}

\int_{2}^{4} y d y = 6

\int_{2}^{4} x y^{2} d y = \frac{56 x}{3}

= 8 + 2 x^{2} + 6 + \frac{56 x}{3}

Vereinfache

= 2 x^{2} + \frac{56 x}{3} + 14

\int_{- 5}^{- 3} x^{2} - 4 d x

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

\int_{0}^{8} 6 x ln (x) d x

\int_{0.5}^{1} 2 x d x

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