Question

What is the integral of \[\dfrac{{dy}}{{dx}}\] ?

Answer 1

Hint: The question so asked is too small to answer. But we are just going to use the basics of integration and derivative here. Given is a derivative and the asked process is to find the integration of it. So we know that the integration and derivative are the opposite processes of each other. And integration of the given function will only give the original function. Let’s solve it!

Complete step by step solution:
Given that,
\[f\left( x \right) = \dfrac{{dy}}{{dx}}\]
Now integrating the function is ,
\[\int {f\left( x \right)} = \int {\dfrac{{dy}}{{dx}}} \]
\[ = y + C\]
This is the integration of the given function.
So, the correct answer is “\[ y + C\]”.

Note: Note that there is no such complicated function given. if we were given with any of those type of function to equate with \[\dfrac{{dy}}{{dx}}\] like if \[\dfrac{{dy}}{{dx}} = 5xy\] then we need to separate the x terms and y terms then and then apply the integration. That on taking integration we would have written constant C like we have written above.