Question:
Solve the integral of $x$ with boundaries $|y-2x|\leq 0.1, 0 \leq x \leq 1, 0 \leq y \leq 1 $
What gave me trouble is the absolute value, I tried graphing it online and got a noncontinuous line, how can I proceed?
2026-04-08 14:32:58.1775658778
Solving the double integral with $|y-2x|\leq 0.1$ as boundary
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Consider $y \geq 2x$ and $2x \geq y$ separately.
Please see the sketch. You have to integrate over the area shaded in black.
Integrate over $dx$ first and then over $dy$ so you have to split it into two integrals otherwise you will have to split it into three.
$D1: 0 \leq x \leq \frac{y + 0.1}{2}, 0 \leq y \leq 0.1$
$D2: \frac{y - 0.1}{2} \leq x \leq \frac{y + 0.1}{2}, 0.1 \leq y \leq 1$