Midterm Exam 2 Solution | Calculus III | MATH 241, Exams of Advanced Calculus

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Math 241 Midterm exam 2 Spring 2014 Ns 3 points) Fill in the blanks in the integrals below that compute the length L of the curve C given by the top half of the ellipse x* — 4y? = 4 (that is, the part of the ellipse that lies on or above the x-axis and connects the two points (2,0) and (—2,0)). Use the parametrization r(t) = (2 cost, sin t) for the ellipse. You do NOT have to evaluate the integral. Hint: Sketch the ellipse and the curve C. Second number in line Line Bi] Line 3] dt First number in line |2) Pencil your answers into the corresponding lines in your Scantron bubble sheet. Line {i}: . = aay? = cos?t—dsin?t See Section \3.3 [2] ©CO@OLO i Res oa @ © /O- $e a) €) = 5 to 7 xX Line [3] “Olam ° ©) = —2sint+cost » © = Bintror . © = V1+3sin7t . ® = 1+3sin't