Question

решите пж интеграл!!!!!!!!!!​

Answer 1

$\displaystyle \int\limits^{4}_{0} {x \cdot \dfrac{1}{36}\left(\frac{x^{3}}{2} + 1 \right) } \, dx = \int\limits^{4}_{0} {\left(\frac{x^{4}}{72} + \frac{x}{36} \right)}\, dx = \left(\frac{x^{5}}{360} + \dfrac{x^{2}}{72} \right) \ \bigg |^{4}_{0} =\\= \frac{4^{5}}{360} + \dfrac{4^{2}}{72} - \left(\frac{0^{5}}{360} + \dfrac{0^{2}}{72} \right) = \frac{1024}{360} + \dfrac{16}{72} = \dfrac{1024 + 80}{360} = \frac{1104}{360} = 3\dfrac{1}{15}$