Mathematics
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OpenStudy (studygurl14):
Antiderivative of.... @mathmale @ganeshie8 @ParthKohli @pooja195 @freckles @mathstudent55 @tkhunny
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OpenStudy (studygurl14):
What do I use for u-substitution?
\(\Large \csc(2x)\cot(2x)\)
OpenStudy (studygurl14):
@mathmale @ganeshie8 @ParthKohli @pooja195 @freckles @mathstudent55 @tkhunny
OpenStudy (er.mohd.amir):
use cos 2x/sin2x *sin2x
put sin 2x=t
OpenStudy (er.mohd.amir):
since csc x=1/sin x and cot x=cosx /sin x
OpenStudy (studygurl14):
Okay, I see what you're saying. I'll try that
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OpenStudy (studygurl14):
Awesome, I think it worked. so far I have 1/u du, which can easily be solved now. Tahnks!
OpenStudy (studygurl14):
wait, no...
OpenStudy (er.mohd.amir):
1/u^2 du
OpenStudy (studygurl14):
the antiderivative of 1/u = ln x
OpenStudy (er.mohd.amir):
there is sin2x is squre
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OpenStudy (studygurl14):
oh, right! two sin 2x. forgot the exponent 2
OpenStudy (studygurl14):
is it -csc 2x?
OpenStudy (studygurl14):
@Er.Mohd.AMIR Is that the correct antiderivative?
OpenStudy (er.mohd.amir):
(-1/2 ) cse 2x
OpenStudy (studygurl14):
how'd you get the 1/2 part?
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OpenStudy (er.mohd.amir):
sin 2x =u
cos 2x .2 .dx=du
OpenStudy (er.mohd.amir):
cos 2x dx=1/2 du
OpenStudy (er.mohd.amir):
got it
OpenStudy (studygurl14):
Oh, I forgot to apply the chainrule when finding du/dx
OpenStudy (studygurl14):
Thank you. :)
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OpenStudy (er.mohd.amir):
welcome