integral from 0 to 3 of sqrt(4-y)

Lösung

\int_{0}^{3} 4 - y d y

\frac{14}{3}

Dezimale

4.66666 \dots

Schritte zur Lösung

\int_{0}^{3} 4 - y d y

Wende U-Substitution an

= \int_{4}^{1} - u d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{4} - u d u

Entferne die Konstante:

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

= - (- \int_{1}^{4} u d u)

Wende die Potenzregel an

= - (- [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{4})

Vereinfache

= [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{4}

Berechne die Grenzen:

\frac{14}{3}

= \frac{14}{3}

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

\int_{- 2}^{0} (8 x^{3} - 7 x^{2}) d x

\int_{- 2}^{2} 3 - ∣ x ∣ d x

\int_{0}^{9} x + 1 d x

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