What if we integrate wrt to y instead of x

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This discussion focuses on the process of integrating functions with respect to different variables, specifically integrating x with respect to y. When x is treated as a constant, the integral of x with respect to y results in xy, similar to integrating a constant c. If x is a function of y, denoted as x = x(y), it is essential to express x in terms of y before performing the integration. This method ensures accurate results in calculus.

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semc
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Hi guys, i was doing some math qn and i found out that i am always integrating like x wrt x so u will get (x^2)/2 right? So i was wondering how do u like say integrate x wrt y?
 
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If x is a constant with respect to y, then the integral of x with respect to y is just xy (just like the integral of c with respect to y is cy when c is a constant). Otherwise, if x depends on y (ie, x=x(y)), then write out x in terms of y and do the integral as usual.
 
alright got it thx
 

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