Particular Antiderivative

Question

Find the particular antiderivative that satisfies the following conditions:

p′(x) = −(80/x^2); p(4)=3.

p(x)= ?

Answer 1

p(x) = ∫p'(x)dx = ∫ [ -80/x²]dx = -80∫x^-2dx = -80(x^-1/-1) + C = 80/x + C

Since p(4) = 3, we have 80/4 + C = 3. So, C = -17.

Therefore, p(x) = 80/x - 17.