Find the area of the region that is bounded by the given curve and lies in...

   

Transcribed Image Text:

Find the area of the region that is bounded by the given curve and lies in the specified sector. 3 3 r = e, < 0 < 4 2 Find the length of the cardioid r = 10 + 10 sin(0). Solution The cardioid is shown in the figure above. Its full length is given by the parameter interval 0 2x, so we have the following. L = 2 dr 2 de de 2 2 2 (10 + 10 sin(0)) + de de We could evaluate this integral by multiplying and dividing the integrand by 2-2 sin(e), or we could use a computer algebra system. In any event, we find that the length of the cardioid is L = 80 Find the area of the region that is bounded by the given curve and lies in the specified sector. 3 3 r = e, < 0 < 4 2 Find the length of the cardioid r = 10 + 10 sin(0). Solution The cardioid is shown in the figure above. Its full length is given by the parameter interval 0 2x, so we have the following. L = 2 dr 2 de de 2 2 2 (10 + 10 sin(0)) + de de We could evaluate this integral by multiplying and dividing the integrand by 2-2 sin(e), or we could use a computer algebra system. In any event, we find that the length of the cardioid is L = 80