## MarcLeclair 2 years ago Integral question ( verifying my answer)

1. MarcLeclair

$\int\limits_{}^{} tsin(t)\cos(t)$ i did as follow: Integration by part u=t and du=dt / dv=sin(t)cos(t) v=sin^2(t)/2 which followed with $(tsin ^{2}t)/2 - \int\limits_{}^{}(\sin ^{2}t)/2dt$ then I get ( just for the integral) $(1/4)\int\limits_{}^{}1-\cos2t \rightarrow (1/4)(t+(\sin2t)/2)$ So my final answer looks like this: $(tsin ^{2}t)/2 - 1/4(t+(\sin2t)/2 + c)$

2. MarcLeclair

The answer key did it differently I just wanted to know if someone could help me confirm whether or not my answer looks right

3. zepdrix

Hmm your process was a little strange. If you start by applying the Double Angle Formula for Sine it makes this problem a bit easier in my opinion. You end up with a solution of,$\large -\frac{1}{4}\cos(2t)+\frac{1}{8}\sin(2t)+C$ But looking at your solution, applying some identities, I can now see that it is equivalent. So it looks like it worked out for you! :)

4. MarcLeclair

Yeah it was a little strange to me, I just remembered a number where it used substitution within the integration by part. I honnestly kinda forgot how to use my substitution to prove a trig ( 3 years ago ) but alright thanks^^ It gets kinda hard to notice whether or not an answer is right when different methods can apply ahaha!

5. MarcLeclair

Yes the solution used double angle so I didn't come up as the same answer!

6. zepdrix

Ah I see c: