Question

how can I integrate this ∫x dy?

Answer 1

xy + C.

treat x as a constant

Answer 2

In this integral the variable x is considered as a constant and would no longer affect the integration.

Answer 3

make sure that it is really 'dy'

if it is dx, then it's the opposite of the differentiation power rule.
if you're subtracting 1 from the nth power with differentiation, you're adding 1 with integration, but you also have to divide it by the new value of the exponent and then +C which basically means that it falls into a group of constant

Answer 4

What's the relationship of x to y? If x and y are both functions of t and you're wanting to integrate along a path you're going to have a different answer altogether...

Answer 5

Suppose it was meant to be integrated along this circle.\[ c(t)=<\cos(t), \sin(t)> \]
\[\int\limits_{c}^{}xdy=\int\limits_{0}^{2 \pi}<0,x,0>*<\frac{ dx }{ dt},\frac{ dy }{ dt},\frac{ dz }{ dt}>dt=\int\limits_{0}^{2 \pi}x\frac{ dy }{ dt}dt\]\[\int\limits_{c}^{}x dy =\int\limits_{0}^{2 \pi}\cos^2(t)dt\]

Just sayin'.

Answer 6

thanks, well, I infered that it's similar to ∫i dt so if is told that i=V/R(e^−t/RC) I don't know how (by substituting the value of i ) then we have V(1−e^−t/RC)