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If $f(x)=\left\{\begin{array}{lll}4 x+3, & \text { if } & 1 \leq x \leq 2 \\ 3 x+5, & \text { if } & 2 \lt x \leq 4\end{array}\right.$ then $\int_1^4 f(x) d x=$
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37
$\begin{aligned} & \int_1^4 f(x) d x=\int_1^2(4 x+3) d x+\int_2^4(3 x+5) d x \\ & =\left|2 x^2+3 x\right|_1^2+\left|\frac{3 x^2}{2}+5 x\right|_2^4=37\end{aligned}$
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