So I do;
dv = cos(x)
v = sin(x)
How do I proceed? It didn't become any simpler after using integration by parts.
A simple sub, not parts. Just in case a picture helps...
... where
... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).
The general drift is...
And the rest...
Spoiler:
_________________________________________
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!
Why use integration by parts when it can be done conveniently with substiution?
Let
you can do the rest!
PS: Does your question specifically tell you to integrate by parts or does it just tell you to integrate the given function? Substitution method is very easy to use in this case
After everything I end up with
Can someone please tell me if this is right? Because the problem is actually one on a definite integral and the answer I get after plugging the numbers is zero, and I don't think that's right...
b = pi
a = 0
You don't have to check with the numbers though, it's enough if you just tell me whether the below is correct;