I have recently been playing with integrals and I still do not fully understand them.(adsbygoogle = window.adsbygoogle || []).push({});

Usually the best way for me to learn is to play with values and figure it out on my own, so I would like you (physics forum) to check my work so far.

After a bit of time I got this:

[tex]\int_{0}^{t}ax^ndx=\frac{at^{n+1}}{n+1}, n\neq-1[/tex]

and after figuring out:

[tex]\int_{0}^{t}ax+bxdx=\int_{0}^{t}axdx+\int_{0}^{t}bxdx[/tex]

I got this equation.

[tex]\int_{0}^{t}ax^n+bx^{n-1}+cx^{n-2} \cdots +ex dx=\int_{0}^{t}ax^ndx+\int_{0}^{t}bx^{n-1}dx+\int_{0}^{t}cx^{n-2}dx \cdots +\int_{0}^{t}(ex)dx=\frac{at^{n+1}}{n+1}+\frac{bt^n}{n}+\frac{ct^n-1} {n-1} \cdots +et[/tex]

Is this true for all polynomials (in standard form)? or does it even work at all?

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# Integral equation. Please check

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