integral from 2 to x of (3t^2-1)

Lösung

\int_{2}^{x} (3 t^{2} - 1) d t

x^{3} - x - 6

Schritte zur Lösung

\int_{2}^{x} 3 t^{2} - 1 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_{2}^{x} 3 t^{2} d t - \int_{2}^{x} 1 d t

\int_{2}^{x} 3 t^{2} d t = x^{3} - 8

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

= x^{3} - 8 - (x - 2)

Vereinfache

= x^{3} - x - 6

\int \frac{csc ^{4} ( 2 x )}{cot ^{2} ( 2 x )} d x

x \to x + 2 lim (2 x^{2} + 3 x - 2)

(\frac{sin ( x )}{x})^{^{'}}

a re a 9 - x^{2}, 0

\int \frac{7 x ^{4} - 6 x ^{2} - x + 5}{x + 2} d x