Integral of sin(2x) | Calculus 1 Exercises

We integrate sin 2x, going over how to compute this integral with u-substitution, and more importantly how to integrate it without writing out the u-substitution. #Calculus1 #apcalculus
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[@justabunga1]

There are 2 acceptable answers also if you rewrite this as a trig identity: sin(2x)=2sin(x)cos(x). There are 2 ways to use the u sub if you let u=sin(x) and du=cos(x)dx. Using the u sub, this rewrites the integral as the integral of 2udu. The answer to that integral is u^2+C=(sin(x))^2+C. You can also let u=cos(x) and du=-sin(x)dx. The integral changes in the form of the integral of -2udu, so the answer is -u^2+C=-(cos(x))^2+C. There are 3 different answers to this if you compare all of these. If you set all of the 3 answers by turning each constant as C_1, C_2, and C_3, you can tell that each of those answers are off by a constant, but the derivative for each of the answer comes out the same way.

[@qmydlsagaming889]

Thank you!

[@user-id4me5xd6m]

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[@user-id4me5xd6m]

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[@WrathofMath]

It is "Lovely" by Crayon Angel from his album "Crickets"! He is an incredible and underrated artist!

[@jasnesciemnienie9107]

Very good explanation, thank you

[@WrathofMath]

Glad it was helpful, thanks for watching!

[@purabus5450]

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[@WrathofMath]

Thank you good commenting guy!

[@Status_video_101]

Why not x^2/2 because after sin integral we do integration of x using chain rule........

[@rohithlohith9495]

was kinday going crazy as to why this isnt happening