## Final Answer

## Step-by-step Solution

Problem to solve:

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Expand the integral $\int_{0}^{2}\left(\frac{1}{2}x+1\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

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$\int_{0}^{2}\frac{1}{2}xdx+\int_{0}^{2}1dx$

Learn how to solve problems step by step online. Integrate the function 1/2x+1 from 0 to 2. Expand the integral \int_{0}^{2}\left(\frac{1}{2}x+1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{2}\frac{1}{2}xdx results in: 1. The integral \int_{0}^{2}1dx results in: 2. Gather the results of all integrals.