I am working on an economics problem where my solution is not correct, and I'd like to know why. Below is the question and my subsequent work/solution:
The demand function for a particular vacation package is $$D(q) = 2000 − 49\sqrt{q}.$$ Find the consumer surplus when the sales level for the package is $800$.
I got this far:
$$CS = \int_0^{800} 2000 - 49q^{1/2}- 614.07dq$$ $$ = \int_0^{800}1386 - 49q^{1/2} dq$$ $$ = 1386q - 24.5q^{-1/2}$$
Did I find the antiderivative incorrectly? I'm not sure what's wrong withn my work.
Note that $\int q^{\frac{1}{2}} dq = \frac{2}{3} q^{\frac{3}{2}} + C$. So you integrated your second term incorrectly.
It should be:
$$\int_{0}^{800} (1386 - 49\sqrt{q}) dq = 1386(800) - \frac{98}{3} \cdot (800)^{\frac{3}{2}}$$