Questions 4 : Integral Differentiation

Question

1. Find the Integral of S 12x² dx
2. Find the total function of S(x² + x⁵) dx
3. A firm uses one input labour (L) to produce output (Q). The marginal product function for the input is MP (L) = 10L^1/2. Find the production function, Q(L).

Answer 1

1. The integral of S 12x² dx is 4x³ + C, where C is the constant of integration.

2. The total function of S(x² + x⁵) dx is x³/3 + x⁶/6 + C, where C is the constant of integration.

3. To find the production function Q(L), we integrate the marginal product function MP(L) = 10L^1/2 with respect to L.

∫10L^1/2 dL = 10 * (2/3)L^(3/2) + C = 20/3 * L^(3/2) + C

Therefore, the production function Q(L) is 20/3 * L^(3/2) + C.