Prove that$$\int_0^2\Big(\int_{y/2}^1e^{-x^2}dx\Big)dy=1-e^{-1}$$ I'm curious how to approach that kind of problems.
2026-04-11 16:50:53.1775926253
Prove that $\int_0^2\Big(\int_{y/2}^2e^{-x^2}dx\Big)dy=1-e^{-1}$
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HINT:
For the integral $\int_0^2\int_{y/2}^1e^{-x^2}\,dx\,dy$ change the order of integration to
$$\int_0^1 \left(\int_{0}^{2x}e^{-x^2}\,dy\right)\,dx$$