Question:
A helicopter rises vertically and t seconds after leaving hte ground its velocity is given in feet per second by v(t) = 8t + 40 / (t+2)² How far above the ground will the helicopter be after 3 seconds?

I assume that I need to integrate the equation to get the helicopter's position. Am I doing this correctly? If so, how can I get the final answer?

Thanks

You are correct, integrate the expression for v(t) to get an expression for the position function s(t). When you do so you introduce a constant of integration C. To find C use the fact that the helicopter is on the ground at time t = 0 seconds, that is s(0) = 0. Write down this equation and solve for C.

Once you know s(t) you can find s(3) which is the hieght of the helicopter after 3 seconds.