integral from-1 to y-1 of 3/2 x^2

Lösung

\int_{- 1}^{y - 1} \frac{3}{2} x^{2} d x

\frac{y ^{3} - 3 y ^{2} + 3 y}{2}

Schritte zur Lösung

\int_{- 1}^{y - 1} \frac{3}{2} x^{2} d x

Entferne die Konstante:

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

= \frac{3}{2} \cdot \int_{- 1}^{- 1 + y} x^{2} d x

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{( - 1 + y ) ^{3}}{3} + \frac{1}{3}

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

Vereinfache

= \frac{y ^{3} - 3 y ^{2} + 3 y}{2}

\int_{- 1}^{2} (1 - ∣ x ∣) d x

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

\int_{1}^{t} \frac{1}{x} d x

\int_{0}^{1} 3 x sin (π) x d x

\int_{0}^{a} arcsinh (t) d t