Solution to intergrals
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Do you think/know that you have solved those incorrectly?
Dr.Peterson
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If you're saying these were assigned in a class, and you don't know what to do other than ask Wolfram Alpha ...
what topics were most recently covered in that class? What theorems might you be expected to apply?
It's hard to help when we don't know anything about what you know. There's a reason for our rules:
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Apologies, it's my first time posting on this forum.
This is a part of a lecture on differential equations. The knowledge of all rules of derivation/ integration is presumed. I just can't see how to solve these two particular steps. I have the solutions and the output given by Wolfram Alpha is correct however I just wanted to understand the steps.
This is a part of a lecture on differential equations. The knowledge of all rules of derivation/ integration is presumed. I just can't see how to solve these two particular steps. I have the solutions and the output given by Wolfram Alpha is correct however I just wanted to understand the steps.
Dr.Peterson
Elite Member
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- Nov 12, 2017
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It would be helpful to know specifically what was taught in this particular lecture. E.g. was it a part of a course on differential equations, or just an introduction to the concept of differential equations within a course on calculus? Were any particular theorems or methods taught? And if there is an image showing how this was actually stated, it could help.
I suspect it may have been about separable differential equations. Perhaps this will help:
Observe that your integral,
has the form [imath]\int f(y) \frac{dy}{dt} dt[/imath]. The page I referred to shows how to do this as a substitution.
I suspect it may have been about separable differential equations. Perhaps this will help:
Differential Equations - Separable Equations
In this section we solve separable first order differential equations, i.e. differential equations in the form N(y) y' = M(x). We will give a derivation of the solution process to this type of differential equation. We’ll also start looking at finding the interval of validity for the solution...
tutorial.math.lamar.edu
Observe that your integral,
has the form [imath]\int f(y) \frac{dy}{dt} dt[/imath]. The page I referred to shows how to do this as a substitution.