C4- Integration question with parametric equations

Edit: Ignore this post. made stupid mistake in calculations

C4 Heinemann Edexcel Mixed Exercise 6L question 15.

The curve shown has parametric equations
$x = 5 \cos \theta, y = 4 \sin \theta$

(The curve is basically an ellipse centred on the origin)

a) Find the gradient of the curve at the point P at which pheta = π/4
b) Find an equation of the tangent to the curve at the point P
c) Find the coordinates of the point R where this tangent meets the x-axis.

Got the first three- easy but it's question d. i'm stuck on.

The shaded region is bounded by the tangent PR, the curve and the x-axis.

d) Find the area of the shaded region, leaving your answer in terms of π.

I know that the tangent meets the x-axis outside the ellipse, to the right of it.
So what I tried was to find the area of the right-angled triangle under PR and subtract from that the definate integral between pheta = 0 and pheta = π/4...

This is the part I'm a bit dubious about because I'm not sure what area the integral would give me. Am I right to use this method? Would it give me the area of the ellipse above the x-axis or below it as well.

Thanks in advance.

I know I’m replying to a message that was years ago but couldn’t help notice no solution was found and I was trying to do this problem so hopefully my method I attached will help someone looking for the way to go about this question.

I know I’m replying to a message that was years ago but couldn’t help notice no solution was found and I was trying to do this problem so hopefully my method I attached will help someone looking for the way to go about this question.

I know I’m replying to a message that was years ago but couldn’t help notice no solution was found and I was trying to do this problem so hopefully my method I attached will help someone looking for the way to go about this question.

Where did the (4sin q)(-5sin q) come from?

*let theta equal

I know I’m replying to a message that was years ago but couldn’t help notice no solution was found and I was trying to do this problem so hopefully my method I attached will help someone looking for the way to go about this question.