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To evaluate the double integral $\displaystyle \int_{0}^{8} \bigg (\int_{(y/2)}^{y/2+1} \bigg (\dfrac{2x-y}{2} \bigg)dx \bigg)dy$ , we make the substitution $u=\bigg (\dfrac{2x-y}{2} \bigg)$ and $v=\dfrac{y}{2}$  The integral will reduce

  1. $\displaystyle \int_{0}^{4} \bigg (\int_{0}^{2}2 \: u \: du\bigg ) dv \\$
  2. $\displaystyle \int_{0}^{4} \bigg (\int_{0}^{1}2 \: u \: du\bigg ) dv \\$
  3. $\displaystyle \int_{0}^{4} \bigg (\int_{0}^{1}u \: du \bigg ) dv \\$
  4. $\displaystyle \int_{0}^{4} \bigg (\int_{0}^{2}u \: du \bigg ) dv$
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