Franklin, your friendly new neighbor, is building a large chicken sanctuary. You decide to help Franklin...

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Franklin, your friendly new neighbor, is building a large chicken sanctuary. You decide to help Franklin build a special chicken coop with volume (in cubic km) given by the integral (²x x√1 - cos(x²) dx. This integral is difficult to evaluate precisely, so you decide to use the methods you've learned this semester to help out Franklin. Your friend and president-elect, Kazilla, stops by to give you a hand. She suggests finding the 4th degree Taylor polynomial, P4(x), for the function 1 - cos(x²) near x = 0. Find P4(x). Substitute P4(x) for 1-cos(x²) in the integral and compute the resulting integral by hand, showing all of your work. Franklin, your friendly new neighbor, is building a large chicken sanctuary. You decide to help Franklin build a special chicken coop with volume (in cubic km) given by the integral (²x x√1 - cos(x²) dx. This integral is difficult to evaluate precisely, so you decide to use the methods you've learned this semester to help out Franklin. Your friend and president-elect, Kazilla, stops by to give you a hand. She suggests finding the 4th degree Taylor polynomial, P4(x), for the function 1 - cos(x²) near x = 0. Find P4(x). Substitute P4(x) for 1-cos(x²) in the integral and compute the resulting integral by hand, showing all of your work.

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