Determine the definite integral of any polynomial.
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Lesson Parent:
Problem:
Determine the definite integral
\[
\int_a^b\,P_n(x)
\]
where $P_n(x)=c_nx^n+c_{n-1}x^{n-1}+\cdots +c_0$.
Answer:
\[\int_a^b\,P_n(x)=\frac{c_n}{n+1}\left\{b^{n+1}-a^{n+1}\right\}+\frac{c_{n-1}}{n}\left\{b^n-a^n\right\}+\cdots+c_0\left\{b-a\right\}\]
