integral from 0 to 2 of t^3(4+t^4)^3

Soluzione

\int_{0}^{2} t^{3} (4 + t^{4})^{3} d t

9984

Fasi della soluzione

\int_{0}^{2} t^{3} (4 + t^{4})^{3} d t

Espandi

t^{3} (4 + t^{4})^{3} : 64 t^{3} + 48 t^{7} + 12 t^{11} + t^{15}

= \int_{0}^{2} 64 t^{3} + 48 t^{7} + 12 t^{11} + t^{15} d t

Applica la Regola della Somma:

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

= \int_{0}^{2} 64 t^{3} d t + \int_{0}^{2} 48 t^{7} d t + \int_{0}^{2} 12 t^{11} d t + \int_{0}^{2} t^{15} d t

\int_{0}^{2} 64 t^{3} d t = 256

\int_{0}^{2} 48 t^{7} d t = 1536

\int_{0}^{2} 12 t^{11} d t = 4096

\int_{0}^{2} t^{15} d t = 4096

= 256 + 1536 + 4096 + 4096

Semplificare

= 9984

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