Giả sử \(\displaystyle\int\limits_{0}^{9}f(x)\mathrm{\,d}x=37\) và \(\displaystyle\int\limits_{9}^{0}g(x)\mathrm{\,d}x=16\). Khi đó, \(I=\displaystyle\int\limits_{0}^{9}\left[2f(x)+3g(x)\right]\mathrm{\,d}x\) bằng
\(122\) | |
\(26\) | |
\(143\) | |
\(58\) |
Chọn phương án B.
Ta có \(\displaystyle\int\limits_{9}^{0}g(x)\mathrm{\,d}x=16\Rightarrow\displaystyle\int\limits_{0}^{9}g(x)\mathrm{\,d}x=-16\).
Khi đó $$\begin{aligned}
I&=\displaystyle\int\limits_{0}^{9}\left[2f(x)+3g(x)\right]\mathrm{\,d}x\\
&=2\displaystyle\int\limits_{0}^{9}f(x)\mathrm{\,d}x+3\displaystyle\int\limits_{0}^{9}g(x)\mathrm{\,d}x\\
&=2\cdot37+3\cdot(-16)\\
&=26.
\end{aligned}$$