Integration with parametic equation

I need help please on question 15)d)

What have you done so far? I'd start by finding the area of the right-angled triangle you've drawn on the figure and subtract from it the area under the curve.

I need help please on question 15)d)

Firstly, it's unclear from the diagram but I think that the required area is just the lower bit that looks like a triangle - not the upper bit with the ink lines on.
There's a neat way and a hackish way. You can find y in terms of x, by finding theta in terms of x and substituting. Alternatively, and much nicer, you can use the formula:
$\displaystyle \int y dx = \int y \frac{dx}{d \theta} d\theta$.

No I used the area formula

Ah, if there's a formula that spits out what you need then feel free to ignore me

No I used the area formula

What area formula

Smaug is correct

You found the limits when you found the co-ordinates of P and R

Because to find the area for intgration , you integrate y with the limits

Yes, as Smaug said

Because to find the area for intgration , you integrate y with the limits

Because to find the area for intgration , you integrate y with the limits

and so you integrate only 4sinx

this is what I mean?

this is what I mean?

this is what I mean?

You haven't actually integrated correctly. You've integrated d(theta) instead of d(x).