Im Kristin
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- Joined
- Apr 12, 2022
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I suspect that the context of the problem would give some hints as to what method you are expected to try. It sounds like you aren't supposed to actually integrate anything, so it's probably some property you are to apply.Hi guys. I need to show these two definite integrals are equal, but I have no idea Can you please have a look? Thanks!
View attachment 32107
Did you see that your two substitution would help? If yes, that is simply brilliant. I knew for a long while that you were amazing but this added on some more. Good job![imath]\dfrac{\cos{x}-\sin{x}}{1+\sin(2x)} = \dfrac{\cos{x}-\sin{x}}{\cos^2{x}+2\sin{x}\cos{x}+\sin^2{x}} = \dfrac{\cos{x}-\sin{x}}{(\cos{x}+\sin{x})^2}[/imath]
[imath]u = \cos{x} + \sin{x} \implies du = (\cos{x} - \sin{x}) \, dx[/imath]
perform the substitution ...