Problem: An art collector purchased for $1000 a painting by an artist whose works are currently increasing in value with respect to time according to the formula dV/dt = 5t^(3/2) + 10t + 50, where V dollars is the anticipated value of a painting t years after its purchase. If this formula were valid for the next 6 years, what would be the anticipated value of the painting 4 years from now? My approach: The first I did is to antidifferentiate the dV/dt. I got V = 2t^(5/2) + 5t^2 + 50t + C. The next step.. I don't quite get it what to replace the value for t. When am I going to use 1000 for V, 6 for t and 4 for t? I believe my answer must be higher than $1000, right? I don't how to substitute the appropriate values. Can you help me with it?