integral from 1 to 2 of e^x-ln(x)

Lösung

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

e^{2} - e - 2 ln (2) + 1

Dezimale

4.28447 \dots

Schritte zur Lösung

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

\int_{1}^{2} e^{x} d x = e^{2} - e

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

= e^{2} - e - (2 ln (2) - 1)

Vereinfache

= e^{2} - e - 2 ln (2) + 1

\int_{0}^{\frac{π}{2}} tan (t) d t

\int_{0}^{\frac{π}{2}} sin^{3} (y) d y

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

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

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