Calcolatore di integrali definiti e impropri
Calcola integrali definiti e impropri passo dopo passo
Il calcolatore cercherà di valutare l'integrale definito (cioè con estremi), inclusi quelli impropri, mostrando i passaggi.
Solution
Your input: calculate $$$\int_{-1}^{2}\left( 13 t^{4} \right)dt$$$
First, calculate the corresponding indefinite integral: $$$\int{13 t^{4} d t}=\frac{13 t^{5}}{5}$$$ (for steps, see indefinite integral calculator)
According to the Fundamental Theorem of Calculus, $$$\int_a^b F(x) dx=f(b)-f(a)$$$, so just evaluate the integral at the endpoints, and that's the answer.
$$$\left(\frac{13 t^{5}}{5}\right)|_{\left(t=2\right)}=\frac{416}{5}$$$
$$$\left(\frac{13 t^{5}}{5}\right)|_{\left(t=-1\right)}=- \frac{13}{5}$$$
$$$\int_{-1}^{2}\left( 13 t^{4} \right)dt=\left(\frac{13 t^{5}}{5}\right)|_{\left(t=2\right)}-\left(\frac{13 t^{5}}{5}\right)|_{\left(t=-1\right)}=\frac{429}{5}$$$
Answer: $$$\int_{-1}^{2}\left( 13 t^{4} \right)dt=\frac{429}{5}\approx 85.8$$$