Question

6. ISec. 13.2] Tom Sawyer's aunt has asked him to whitewash both sides of an old fence. The fence line on the ground is in the shape of C(t) = (30os3 t, 30 sin3 t) with 0 < t < π. The fence reaches up to the function f(13)-1 + (y/3). Tom estimates that for each 25 square feet of whitewashing he lets someone do for him, the willing victim will pay 5 cents. How much can Tom hope to earn, assuming his aunt will provide the whitewash free of charge? You may find it helpful to see what this curve, a type of hypocycloid known as an astroid, looks like. A picture of an astroid can be found on page 127 in the text and Wikipedia has a sweet animation of how this curve is generated.

I'm having difficulty evaluating the integral. The answer is 180 cents.

Answer 1

6 Sdution 0 Nen ence 1S dom riqin 未 e made. he e by tt dt The hish at each point s en by oe t ,T) the e Sence sie ageaO

rks will be ameaimattr be 옛ulb Area toin be pained Amount d l be equal to 389 43 paun pee Exe