Urgent help C4 trig addition formulae & integration

Hi I'm really stuck on this particular question:

Evaluate exactly the integral:

Integral sign with limits 2pi/3 and pi, then the expression is 1/2sin(theta-(pi/3)).
I'm thinking of converting it into a log expression like ln 2sin(theta-(pi/3)) ???

Would appreciate some help please!

The derivative of things like sin(x-pi/2), you just need to apply the chain rule and you get cos(x-pi/2).

Does that help you with your integral?

Hi I don't see how differentiating can help with the integral :/ I know 2sin(theta-(pi/3)) differentiates to 2cos(theta-(pi/3)) but can't see what to do next..

Differentiating and integrating are the reverse of eachother. It's supposed to be an indirect hint.

Using what you've just said, what do you think (1/2) * sin(theta-(pi/3)) integrates to?

1/2 * (-cos(theta-(pi/3))?? Sin integrates to -cos right?

Yes, well done.

So I just sub in the limits into that, simplify then I'm done?

You've got your expression for the integral so I don't see why not

Ok thanks for the help, much appreciated

No worries.

Hey sorry to bother you again but can 1/2 be taken out of the integral sign? As the expression is 1/(2*sin(theta-(pi/3)))

Ah, it is a case of ambiguous equations then it wasn't clear that 1/2sin(theta-(pi/3)) is 1/(2*sin(theta-(pi/3)).

1/2 can be taken out to give (1/2) * the integral of (1/(sin(theta-(pi/3)))).

What would that integral be?

Ah, it is a case of ambiguous equations then it wasn't clear that 1/2sin(theta-(pi/3)) is 1/(2*sin(theta-(pi/3)).

1/2 can be taken out to give (1/2) * the integral of (1/(sin(theta-(pi/3)))).

What would that integral be?

Isn't it ln when you've integrating 1/something?

That is what it seems like you are integrating, but it is unclear.

Please use latex if you can, or post a picture of the question, or type it out in a more understandable way as I do not know what the question is.

Sorry about the shadow xD

Sorry about the shadow xD

Sorry about the shadow xD