Solomon paper A - I need help

Can anyone help me with this question?

What have you done so far for part c?

Can anyone help me with this question?

i actually do not know how to start or where to start from

You know that the area is $\displaystyle \int_a^b y \, \mathrm{d}x = \int_a^b y \, \frac{\mathrm{d}x}{\mathrm{d}t} \, \mathrm{d}t$

So you can replace $y$ and $\frac{\mathrm{d}x}{\mathrm{d}t}$ by their respective expressions and the limits should follow from from $x=0$ at which you need to find the value of $t$ that makes this so and then do the same for the other limit (which you've cropped out of the question, so...)

You've been given parametric equations, you can make it $\frac{dy}{dx}$ by differentiating $x=cos2t$ and $y=cosect$.

Anyways, I'm assuming you should've done part a and b.

Find what $t$ equals when $x=0$ .

This will be your limits for when you integrate to find the shaded area.

I hope this helps you start of?

Oh, I get it - Thanks mate
what about 6 a? I tried solving it by parts but it seems I am missing something

Oh, I get it - Thanks mate
what about 6 a? I tried solving it by parts but it seems I am missing something

Oh, I get it - Thanks mate
what about 6 a? I tried solving it by parts but it seems I am missing something

I tried integration by parts too and got .

Doesn't look right though. is another answer I got.

I'm sorry but I'm not great at integration by parts yet. Maybe the way you did it is wrong? What exactly did you do step by step when integrating?