Integrate the function $2-x-2y$ from $\frac{x}{2}$ to $1-\frac{x}{2}$

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$\int_{\frac{x}{2}}^{\left(1+\frac{-x}{2}\right)}2dy+\int_{\frac{x}{2}}^{\left(1+\frac{-x}{2}\right)}-xdy+\int_{\frac{x}{2}}^{\left(1+\frac{-x}{2}\right)}-2ydy$

Learn how to solve differential calculus problems step by step online. Integrate the function 2-x-2y from x/2 to 1-x/2. Expand the integral \int_{\frac{x}{2}}^{\left(1+\frac{-x}{2}\right)}\left(2-x-2y\right)dy into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{\frac{x}{2}}^{\left(1+\frac{-x}{2}\right)}2dy results in: 2\left(1+\frac{-x}{2}\right)-x. The integral \int_{\frac{x}{2}}^{\left(1+\frac{-x}{2}\right)}-xdy results in: \left(-1+\frac{x}{2}\right)x+\frac{x^2}{2}. Gather the results of all integrals.