- #1

MexterO

- 12

- 0

Hi Everyone, I have a question on u-substitution it's a conceptual one.

Let's say I have the integral ∫x-y dx. where y is strictly just some constant, very simple integral.

I know the integration for that is simply (x^2)/2 - yx.

However, my classmate told me that I could use u-substitution. I told him you could either

do this in your head or use the concept of linearity for integrals. I said it would be silly to use u substitution.

I find it peculiar though since if I use u substitution on this problem I get a whole different anti-derivative.

I let u = x-y and I get du = dx, I then substitute it in and I get of course the anti derivative to be equal to ((x-y)^2)/2.

What is going on here, am I forgetting something or am I breaking a calculus rule?

Let's say I have the integral ∫x-y dx. where y is strictly just some constant, very simple integral.

I know the integration for that is simply (x^2)/2 - yx.

However, my classmate told me that I could use u-substitution. I told him you could either

do this in your head or use the concept of linearity for integrals. I said it would be silly to use u substitution.

I find it peculiar though since if I use u substitution on this problem I get a whole different anti-derivative.

I let u = x-y and I get du = dx, I then substitute it in and I get of course the anti derivative to be equal to ((x-y)^2)/2.

What is going on here, am I forgetting something or am I breaking a calculus rule?

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