Find each double integral over the rectangular region $R$ with the given boundaries. $$\iint_{R} \sqrt{x+y} d y d x ; 1 \leq x \leq 3,0 \leq y \leq 1$$

Okay, so we want to evaluate this double integral over this region. Rectangular region of the function X squared Plus for why cube The wild yaks in the region is that's rectangle wonder too in the X and zero to three and the y Okay, so this is just And the exits one, too. In the UAE, Syria to three X squared plus four. Why, kid, The wide the X So that's one two anti derivative with respect to why we give why X squared. Plus, why'd the fourth evaluated from zero to three the ex? Okay, I want to It's gonna be three next squared. Plus Okay, three to the fourth is eighty one. Okay, I'LL take another anti derivative with respect to X. So we have one too. Could be X. You actually take the anti derivative here. Execute plus eighty one x evaluated from one to two. Well, excuse. Evaluated from one to two is just to keep my eyes. One cube. So that should be, uh, see a minus one to seven and then plus eighty one evaluated X value. It from one to two is just one. So let's just take one. It's in. The final answer is a

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## Video Transcript

Okay, so we want to evaluate this double integral over this region. Rectangular region of the function X squared Plus for why cube The wild yaks in the region is that's rectangle wonder too in the X and zero to three and the y Okay, so this is just And the exits one, too. In the UAE, Syria to three X squared plus four. Why, kid, The wide the X So that's one two anti derivative with respect to why we give why X squared. Plus, why'd the fourth evaluated from zero to three the ex? Okay, I want to It's gonna be three next squared. Plus Okay, three to the fourth is eighty one. Okay, I'LL take another anti derivative with respect to X. So we have one too. Could be X. You actually take the anti derivative here. Execute plus eighty one x evaluated from one to two. Well, excuse. Evaluated from one to two is just to keep my eyes. One cube. So that should be, uh, see a minus one to seven and then plus eighty one evaluated X value. It from one to two is just one. So let's just take one. It's in. The final answer is a

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