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Beliebt Rechnen >

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

Lösung

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

Lösung

e + \frac{10}{3} - \frac{1}{e}

+1

Dezimale

5.68373 \dots

Schritte zur Lösung

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

Vereinfache

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

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

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

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

= e - \frac{1}{e} - \frac{2}{3} + 4

Ziehe Brüche zusammen

4 - \frac{2}{3} : \frac{10}{3}

= e + \frac{10}{3} - \frac{1}{e}

Graph

Beliebte Beispiele

(dy)/(dx)= 1/(xln(2))

\frac{d y}{d x} = \frac{1}{x ln ( 2 )}

derivative 3e^{2x^2}

d er i v a t i v e 3 e^{2 x^{2}}

derivative of (2x+3^3)

\frac{d}{d x} ((2 x + 3)^{3})

(\partial)/(\partial x)(r(θ,x)sin(θ))

\frac{\partial}{\partial x} (r (θ, x) sin (θ))

fläche x=5,y=sqrt(5x)

a re a x = 5, y = 5 x