Science:Math Exam Resources/Courses/MATH101/April 2015/Question 08 (b)/Solution 1

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Since the region is symmetric around the y-axis so we conclude that .

(Indeed, and is even function, so that from the formula for we can easily see this.)

To find the y-coordinate we use the formula given in Hint (1). Note that from part (a) the area of the region is and

Center of mass: