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

Lösung

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

\frac{1}{2} + \frac{π}{2}

Dezimale

2.07079 \dots

Schritte zur Lösung

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

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

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

= \frac{1}{2} + \frac{π}{2}

\int_{0}^{1} \frac{1}{4 + 5 x - 1} d x

\int_{0}^{5} \frac{x}{x ^{2} + 1} d x

\int_{4}^{5} 1

\int_{1}^{e^{x}} 2 ln (t) d t

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