integral from 0 to 2 of (sin(x)+e^x)

Lösung

\int_{0}^{2} (sin (x) + e^{x}) d x

e^{2} - cos (2)

Dezimale

7.80520 \dots

Schritte zur Lösung

\int_{0}^{2} sin (x) + e^{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}^{2} sin (x) d x + \int_{0}^{2} e^{x} d x

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

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

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

Vereinfache

= e^{2} - cos (2)

\int (x^{2} (x^{3} - 2 x + 1)) d x

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 6}{x})

\int \frac{1}{x ^{3} + x ^{2}} d x

\int \frac{29 x ^{4} + 29 x ^{3} + 2 x + 1}{x ^{2} + x} d x

\frac{d}{d x} y = (sin (\frac{x}{2}) - cos (\frac{x}{2}))^{2}