Question

Find the equation of the curve which passes through the point (2,3) and for which dy/dx=3x^2+x.

Answer 1

take the antiderivative of 3x^2+x, then find C so that it passes through (2,3)

Answer 2

antiderivative or indefinite integral, I forget which

Answer 3

Is it:

dy/dx=3(2)^2+2=14
integrate dy/dx= x^3+x^2/2+c
using pt (2,3),
3=2^3+2^2/2+c
c=-3

Answer 4

Therefore the eqn is: y=x^3+x^2/2-3

Answer 5

Is it right?

Answer 6

check finding c again...

Answer 7

but I may be wrong.

Answer 8

c =-7 friend, so the equation is y = x^3 + x^2/2 -7