Help urgent maths

I don’t get why the 1/2 comes out of the integral
I got this but idk how

cant see an attachment but you can take constants out of the integral as if you're taking it outside brackets

Hey I just added it in

taking the 1/2 outside the integral won't change the answer you get it just makes the working easier. if you have left the half inside the integral and got the wrong answer then your working has gone wrong somewhere

Is my working right then?

did you get the right answer if you expand the brackets to the power of 3/2. if you didnt get the right final answer then no. if you need help integrating it let me know

I got the wrong answer plz help

does the question ask you to use small angle approximation to integrate? can you attach it please?

Cos theta equals 1-(theta)squared over 1
I’ve not got it rn but it’s just the cos theta one u can search it up

no i mean does the question specify you have to use this or can you just integrate root cosx. and are you able to upload the actual question

Yeah the q says use this, I’ve lost the question now sorry but can u help with what’s given plz 😭

Your working looks like complete nonsense tbh - try differentiating what you've written and see if gives you back the thing you're trying to integrate!

All they've done is apply a binomial approx to the square root in the integral and then integrate the resulting expression. I'm not actually sure why they took the 1/2 outside the integral just to put it back in again, but it doesn't change the answer!

I used the chain rule but idk

The chain rule is for differentiation, not integration. If you differentiate your answer, you should get back to the thing inside the integral (the "integrand"), whereas you will actually get back something horrible! they're actually trying to help you in this question by using a binomial approximation which is easy to integrate

I’m stuck… I don’t know what to do after this