Giải thích các bước giải:

Câu 23:

Ta có:

$\begin{aligned}
& h(x) = 3 - \dfrac{2}{5}x \\
& \text{Đáy} = 2h(x) \\
& S(x) = \dfrac{2}{3} \cdot \text{Đáy} \cdot h(x) = \dfrac{2}{3} \cdot 2h(x) \cdot h(x) = \dfrac{4}{3} \left(3 - \dfrac{2}{5}x\right)^2 \\
& V = \int_{0}^{5} S(x) \text{d}x \\
& V = \int_{0}^{5} \dfrac{4}{3} \left(3 - \dfrac{2}{5}x\right)^2 \text{d}x \\
& V = \dfrac{4}{3} \cdot \left[ \dfrac{1}{-\dfrac{2}{5}} \cdot \dfrac{\left(3 - \dfrac{2}{5}x\right)^3}{3} \right]_{0}^{5} \\
& V = \dfrac{4}{3} \cdot \left( -\dfrac{5}{2} \right) \cdot \dfrac{1}{3} \left[ \left(3 - \dfrac{2}{5} \cdot 5\right)^3 - (3 - 0)^3 \right] \\
& V = -\dfrac{10}{9} \left( 1^3 - 3^3 \right) \\
& V = -\dfrac{10}{9} (1 - 27) \\
& V = \dfrac{260}{9}
\end{aligned}$