Total cost from marginal cost via the Net Change Theorem

By the Net Change Theorem, the total cost of producing 200 units equals $\int_0^{200} MC(x)\, dx = C(200) - C(0)$, where $C(x)$ is an antiderivative of $MC(x)$. An antiderivative of $50 - 0.1x$ is $C(x) = 50x - 0.05x^2$ (plus a constant, which cancels in the definite integral).

Evaluating: $C(200) = 50(200) - 0.05(200)^2 = 10000 - 2000 = 8000$, and $C(0) = 0$. Therefore the total cost is $8000 - 0 = 8000$ dollars, meaning it costs $8000 to produce the first 200 units.