Use A = int_a^b(y_1(x)y_2(x))dx where y_1(x) >= y_2(x) Find the x coordinates of endpoints of the area 6x x^2 = x^2 2x 0 = 2x^28x x = 0 and x = 4 This means that a = 0 and b = 4 Evaluate both at 2 and observe which is greater y = 6(2)(2)^2 = 8 y = 2^2 2(2) = 0 The first one is greater so we subtract the second from the first in the integral int_0^4(6xx^2) (x^2 2x)dx Find the centroid of each simple region Replace each region with a point mass at its centroid, where the mass is the area of the region Find the centroid of these point masses (this is done by taking a weighted average of their x and y coordinates) This is easiest to see with an example ExampleRead how Numerade will revolutionize STEM Learning
How To Find Centroid Of A Parabolic Spandrel By Integration Youtube
