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Beliebt Rechnen >

integral from t-1 to 2 of-t+2

Lösung

\int_{t - 1}^{2} - t + 2 d t

Lösung

- 2 t + \frac{1}{2} (t - 1)^{2} + 4

Schritte zur Lösung

\int_{t - 1}^{2} - t + 2 d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{t - 1}^{2} t d t + \int_{t - 1}^{2} 2 d t

\int_{t - 1}^{2} t d t = 2 - \frac{( t - 1 ) ^{2}}{2}

\int_{t - 1}^{2} 2 d t = - 2 t + 6

= - (2 - \frac{( t - 1 ) ^{2}}{2}) - 2 t + 6

Vereinfache

- (2 - \frac{( t - 1 ) ^{2}}{2}) - 2 t + 6 : - 2 t + \frac{1}{2} (t - 1)^{2} + 4

= - 2 t + \frac{1}{2} (t - 1)^{2} + 4

Beliebte Beispiele

derivative f(x)=(2x+3)^3

d er i v a t i v e f (x) = (2 x + 3)^{3}

derivative of 1+3x

\frac{d}{d x} (1 + 3 x)

integral of (x^2-2x+1)e^{2x}

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

limit as x approaches pi of 2cot(x)

x \to π lim (2 cot (x))

integral of e^{t^3}

\int e^{t^{3}} d t