Hi everyone! I have two questions, one about area of surface of revolution and another is about arc length...
I really fail to do this two question despite many times of trying so I hope someone can help me
1. Find the area of the surface of revolution generated by revolving the arc of the cardioid " x = 2 cos k - cos 2k, y = 2 sin k - sin 2k " about the X-axis.
2. A warehouse is 75m long and 40m wide. A cross-section of the roof is the inverted catenary y = 31 - 10 (e^0.05x + e^-0.05x). Find the number of square metres of roofing in the warehouse. Hint: Find the arc length of the catenary and multiply this by the length of the warehouse.
I would be really grateful if you can help me
Remember that cosine is an even function, so :
Your other question I can address later when I have more time. For now, note that I used hyperbolic functions to make the integration smoother. You could leave it in exponential form though.