4. [-11 Points] DETAILS LARAPCALC10 5.1.047.M|. Find the particular solution that satisfies the differential equation and the initial condition. f'(x) = 12x3 4x; f(1) = 1 f(X) = 10. [-/1 Points] DETAILS LARAPCALC10 5.4.505.XP. Find the area of the region. y = 6ex/2 40 30 20 10/ X 1 2 3 4 5 A11. [-/1 Points] DETAILS Find the average value of f(x) = + on the closed interval [1, 4]. O O 6 O 6 O O12. [11 Points] ' DETAILS l LARAPCALC105.5.002. Find the area of the region. See Examples 1, 2, 3, and 4. 1'00 =x2+6x+9 g(x) = 6X+ 25 13. [11 Points] DETAILS LARAPCALC1O 5.5.001. Find the area of the region. See Examples 1, 2, 3, and 4. f(X) = x2 8x 9(X) = 0 The graph of y = f(x) is shown below. Given that the area of region A is l, the area of B is 3 and I: Hz) at: = %, what is [23 f(x) dz