The arc of the parabola joining the points and is rotated through radians about the x-axis. Find the area of the curved surface generated giving the answer in the form where k is an integer.
My attempt at answering it is written down here:
I'm not sure if it's right because if it wants an answer in that form, then it would suggest that the integer k isn't divisible by 3 - otherwise it could be simplified. Through that logic, I believe I have made some kind of mistake. Could you please take a look and suggest any area where I have slipped up?
Thanks for your help and time if you can answer
Thanks for your solution! I can see what you've done for the most part, only the part which is in the fourth and fifth lines I can't seem to understand. I see you differentiated it after reducing to but differentiating it implicitly gives the same thing once simplified - I see what has happened by there.
I cannot see how you have got it into that particular form. Please could you show me what you have done there more closely?
I can see you took the 2 out as a constant to get but can't see how it simplifies to .