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?(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Problems on Antidifferentiation

**Physics Forums | Science Articles, Homework Help, Discussion**