integral from-1 to 0 of (4+sqrt(1-x^2))

Lösung

\int_{- 1}^{0} (4 + 1 - x^{2}) d x

4 + \frac{π}{4}

Dezimale

4.78539 \dots

Schritte zur Lösung

\int_{- 1}^{0} 4 + 1 - x^{2} d x

Wende die Summenregel an:

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

= \int_{- 1}^{0} 4 d x + \int_{- 1}^{0} 1 - x^{2} d x

\int_{- 1}^{0} 4 d x = 4

\int_{- 1}^{0} 1 - x^{2} d x = \frac{π}{4}

= 4 + \frac{π}{4}

\int_{0}^{4} π (x - 1) d x

\int_{1}^{2} (2 x^{3} - x^{4}) d x

\int_{0}^{1} x (e^{x}) d x

\int_{1}^{3} y^{2} d y

\int_{1}^{2} (2 x + \frac{2}{x ^{2}}) d x