- #1
Karol
- 1,380
- 22
Homework Statement
Homework Equations
$$\frac{dy}{dx}=f(x)~\rightarrow~dy=f(x)dx~\rightarrow~y=\int f(x)dx$$
The Attempt at a Solution
If the interpretation of an integral is the derivative at that point, x1 for example, then these can't all be solutions since the tangent, the derivatives, at x1 are different.
The constant C can't compensate for that since it shifts the graph up or down, not to the sides, as the solutions ##~\sin^2x+C_1## and ##~\cos^2x+C_2## are, but the solution ##-\frac{1}{2}\cos(2x)+C_3## is neither that nor that.