Hàm số \(f\left(x\right)\) thỏa mãn \(\int\limits^9_0f\left(x\right)dx=9\). Khi đó \(\int\limits^3_0f\left(3x\right)\text{d}x\) bằng
\(\int\limits^3_0f\left(3x\right)\text{d}x=3\). \(\int\limits^3_0f\left(3x\right)\text{d}x=27\). \(\int\limits^3_0f\left(3x\right)\text{d}x=-3\). \(\int\limits^3_0f\left(3x\right)\text{d}x=1\). Hướng dẫn giải:Đặt \(x=3t\) khi đó \(\text{d}x=3\text{dt}\), \(x|^9_0\Rightarrow t|^3_0\)
\(\int\limits^9_0f\left(x\right)dx=\int\limits^3_0f\left(3t\right)\text{3dt}=3\int\limits^3_0f\left(3t\right)\text{d}t=3\int\limits^3_0f\left(3x\right)\text{d}x\)
Suy ra \(\int\limits^3_0f\left(3x\right)\text{d}x=\frac{1}{3}\int\limits^9_0f\left(x\right)dx=\frac{1}{3}.9=3\).