Cho $\int\limits_{1}^{2}{f\left( x \right) }\text{d}x=100$. Khi đó...

$\int\limits_{1}^{2}{\left[ 3f\left( x \right)+4 \right]} \text{d}x$ $=3\int\limits_{1}^{2}{f\left( x \right)} \text{d}x+4\int\limits_{1}^{2}{\text{d}x}$ $=300+\left. 4x \right|_{1}^{2}$ $=300+\left( 4.2-4 \right)$ $=300+4$ $=304$.