Integration by Parts - example 1 : ExamSolutions

[jericlora]

..sir can i ask how u get 1/2 cos 2x?

[ExamSolutions]

@jericlora Because that is the integral of sin 2x (excluding the minus sign)

[KevinPaul06]

Can I ask you? How did you know the the integral of "cos2x"? Well, of course yo studied it :P . Ahmm can you give a link or tutorial about it?

[gimmecola]

@KevinPaul06 Just consider what we would differentiate to get cos2x. The derivative of sin(X) is (d/dX)cos(X) according to the product rule. In this particular instance, we have X = 2x. d/dx(2x) = 2, therefore the derivative of sin2x is 2cos2x. However, seeing as we only have (1)cos2x, we know that we must divide the coefficient by two to give the integral, thus (1/2)sin2x.

[neozmatrix]

God bless you sir!! All your videos are so easy to understand.... Keep up the good work.

[tomyo669]

All the other guides suck this is the only one that explains integration by parts

[TravisKPHall]

thankyou

[ExamSolutions]

@TravisKPHall That's ok

[JKT6]

how do you know when to use this or when to use substitution sir?

[fmawson]

@JKT6 in exams, they'll usually prompt you to use substitution so if they give you no prompt (or if they say integrate by parts) then you should integrate by parts.

[JKT6]

@fmawson ha cool thanks :D

so it will be very clear on which to use,

isit true you can actually use by parts for any of the integration questions get a solution?

[fmawson]

@JKT6 Im not sure, the exam solutions guy probs knows better than me. I mean, you could, in theory, include 1 as a factor, for example, (1)(lnx) and integrate 1 whilst differentiating lnx. If theres only one factor though, it'll usually just make it more unnecessarily difficult doing it by parts.

[cesfigas]

Goood very good

[DJPirrone]

By parts in C4?