∫(0,π)|sinx-cosx|dx
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∫(0,π)|sinx-cosx|dx∫(0,π)|sinx-cosx|dx∫(0,π)|sinx-cosx|dx∫(0,π)|sinx-cosx|dx=∫(0,π)√2|sin(x-π/4)|dx=
∫(0,π)|sinx-cosx|dx
∫(0,π)|sinx-cosx|dx
∫(0,π)|sinx-cosx|dx
∫(0,π)|sinx-cosx|dx
=∫(0,π)√2|sin(x-π/4)|dx
=-∫(0,π/4)√2sin(x-π/4)dx+∫(π/4,π)√2sin(x-π/4)dx
=-[-√2cos(x-π/4)](0,π/4)+[-√2cos(x-π/4)](π/4,π)
=[√2cos(x-π/4)](0,π/4)-[√2cos(x-π/4)](π/4,π)
=√2-1-[(-1)-√2]
=2√2
∫(0,π)|sinx-cosx|dx
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