Understanding Integrals: Multiplying by a Constant Within the Integral?

[Fritz]

if you have $$\int_frac{y}{x}=int_L$$, if you multiply the LHS by c within the integral, is L multiplied by c within its integral?

 

[chroot]

Do you mean this?

$$\int \frac{y}{x} = \int L$$

- Warren

 

[marlon]

or are you talking about multiplying some constant with an integral ?

- Marlon

$$c * \int\frac {y}{x} = \int cL$$ ?

 

[Fritz]

Not a constant, another variable.

 

[HallsofIvy]

If you mean "Is $f(x)\int g(x)dx= \int f(x)g(x)dx$" the answer is no:
$x\int xdx= \frac{1}{2}x^3+ C$ and $\int x^2dx= \frac{1}{3}x^3+ C$.

I may be misunderstanding your question since if you are taking differential equations, you certainly should know calculus enough that that would be obvious.

 

[JonF]

Stewart has a first order differential equation section in 2nd semester calculus.