integral from 0 to 1 of 1-sqrt(x)

Lösung

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

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

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

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

\int_{0}^{1} x d x = \frac{2}{3}

= 1 - \frac{2}{3}

Vereinfache

1 - \frac{2}{3} : \frac{1}{3}

= \frac{1}{3}

\int_{1}^{x} \frac{1}{1 + t ^{3}} d t

\int_{- x}^{x} x + y d y

\int_{0}^{1} - x^{2} - x^{3} + 2 x d x

\int_{- 2}^{x} (28 t^{2} - 27 t) d t

\int_{1}^{5} (\frac{8}{x} - e^{- x}) d x