The area of the region bounded by the curves y = |x-1| + |x-3| and y = 6 - |x-2| is equal to

Step-by-step solution

Let f(x) = |x-1| + |x-3| and g(x) = 6 - |x-2| . First, we write the piecewise definitions of both functions: f(x) = 4 - 2x for x f(x) = 2 for 1 x 3 f(x) = 2x - 4 for x > 3 g(x) = 4 + x for x 2 g(x) = 8 - x for x > 2 Next, we find the points of intersection of y = f(x) and y = g(x) . For x For x > 3 : 2x - 4 = 8 - x 3x = 12 x = 4 . At x = 4 , y = 4 . Checking the interval [1, 3] shows no other intersection points. The required area is bounded between x = 0 and x = 4 . Required Area = ₀⁴ (g(x) - f(x)) dx We can compu