View an example | All parts showing X Find the area between the curve and the x-axis over the indicated interval. y = 144 -x ; [- 12, 12] To find the area under the graph of a nonnegative, continuous function f over the interval [a,b], find any antiderivative F(x) of f(x). Then evaluate F(x) using b and a, and compute F(b) - F(a). The result is the area under the graph over the interval [a, b]. In this case, f(x) = 144 - x", with a = - 12 and b = 12. The general form of the antiderivative of f(x) = 144 - x is F(x) = 144x - 3X The simplest antiderivative is the one for which the constant of integration is 0, so use F(x) = 144x - x 3 Substitute 12 and - 12, and find the difference F(12) - F( - 12). First find F(12). F(12) = 144 . 12 - 5 . 123 = 1152 Now find F( - 12). F( - 12) = 144 . (- 12) - 3 . (-12)3 = - 1152 Subtract to find the area over [ - 12, 12]. Area over [ - 12, 12] = F(12) - F( - 12) = 1152 - (-1152) = 2304 Thus, the area under the curve is 2304.Find the area between the curve and the x-axis over the indicated interval. y = 49 -x ; [-7.7] The area under the curve is .(Simplify your answer.)