What do I do with the coefficient when doing integrals?

Question

In the problem,

"y=6 cos x", do I just find the integral of "cos x" or do I do something with the 6?

Answer 1

There is a property of integrals which says

∫(6 cos (x) dx) = 6∫(cos (x) dx).

That is, to find the indefinite integral of 6 cos (x), you can just find the indefinite integral of cos (x) and multiply it by 6. (This will, of course, give you the answer 6 sin (x) + C. )

This property of integrals applies whenever you have a constant coefficient (like 6) in front of a function.

Answer 2

Leave the 6. As in, the integral of 6cos(x) is 6sin(x). The point of an integral is, "What would I take the derivative of to get this?" So, if we take the derivative of 9x^2 we get 18x, so the integral of 18x must be 9x^2.

Answer 3

just do like these
6∫cosx dx