Find the centroid of the region bound by y = x + 3 and y = x² - 3. A) (0, 1.68) B) (1.098, 1.68) C) (0, 4) D) (1.68, 1.098) E) (0, 2.18)

Question

Quizplus · Accepted Answer

The centroid of a region bounded by two curves can be found by integrating the functions over the interval where they intersect. The intersection points of y = x + 3 and y = x^2 - 3 are x = -3 and x = 2. The centroid (x̄, ȳ) is calculated using the formulas for x̄ and ȳ, which involve integrating the difference of the functions over the interval. The correct centroid is approximately (1.098, 1.68).

Find the Centroid of the Region Bound by Y =