1. Find the particular antiderivative that satisfies the following conditions:
2. Find the particular antiderivative that satisfies the following conditions:
3. A particle is moving as given by the data below:
where is the position, and is the velocity.
Integrate both sides.
The integral of dR/dt is R. The integral of 40/t^2 is . Now you know that R = -40/t + C And when t = 1, R = 40. So, it follows that C = 40 + 40 = 80. Therefore, the particular integral (or antiderivative) is R(t) = -40/t + 80.
Same thing. Integrate both sides.
p'(x) is really dp/dx. Its integral is p. You can find out the integral of 40/x^3. Do NOT forget the +C (there are no limits), or else you won't get a 'particular' integral. You know that p(4) = 4. That means, when x = 4, p = 4 as well. Find C, then get the particular integral.
I hope that helps.
P.S. Give it a try, show how you worked it out, and we'll help you out.