integral from 0 to x^2 of e^xf(t)

Lösung

\int_{0}^{x^{2}} e^{x} f (t) d t

\frac{x ^{4} f e ^{x}}{2}

Schritte zur Lösung

\int_{0}^{x^{2}} e^{x} f t d t

Entferne die Konstante:

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

= f e^{x} \cdot \int_{0}^{x^{2}} t d t

Wende die Potenzregel an

= f e^{x} [\frac{t ^{2}}{2}]_{0}^{x^{2}}

Berechne die Grenzen:

\frac{x ^{4}}{2}

= f e^{x} \frac{x ^{4}}{2}

Vereinfache

= \frac{x ^{4} f e ^{x}}{2}

\int_{\frac{- 8}{7}}^{\frac{8}{11}} \frac{7}{4} x + 2 d x

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

\int_{- 1}^{0} x^{2} (x - 2) d x

\int_{- 1}^{1} (10 x^{2} + 11) d x

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